if i click a columns,it will be sorted ascending,then i click a same columns
again,it will be sorted descending.

Hello,

There is a Microsoft Knowledge Article (KB) describing it in detailed. You
may get it from the link below:

HOW TO: Sort a ListView Control by a Column in Visual C# .NET (Q319401)
http://support.microsoft.com/default.aspx?scid=kb;EN-US;q319401

For your convenience, I have pasted a snip of code here:

using System.Collections;      
using System.Windows.Forms;

/// <summary>
/// This class is an implementation of the 'IComparer' interface.
/// </summary>
public class ListViewColumnSorter : IComparer
{
        /// <summary>
        /// Specifies the column to be sorted
        /// </summary>
        private int ColumnToSort;
        /// <summary>
        /// Specifies the order in which to sort (i.e. 'Ascending').
        /// </summary>
        private SortOrder OrderOfSort;
        /// <summary>
        /// Case insensitive comparer object
        /// </summary>
        private CaseInsensitiveComparer ObjectCompare;

        /// <summary>
        /// Class constructor.  Initializes various elements
        /// </summary>
        public ListViewColumnSorter()
        {
                // Initialize the column to '0'
                ColumnToSort = 0;

                // Initialize the sort order to 'none'
                OrderOfSort = SortOrder.None;

                // Initialize the CaseInsensitiveComparer object
                ObjectCompare = new CaseInsensitiveComparer();
        }

        /// <summary>
        /// This method is inherited from the IComparer interface.  It compares
the two objects passed using a case insensitive comparison.
        /// </summary>
        /// <param name="x">First object to be compared</param>
        /// <param name="y">Second object to be compared</param>
        /// <returns>The result of the comparison. "0" if equal, negative if 'x'
is less than 'y' and positive if 'x' is greater than 'y'</returns>
        public int Compare(object x, object y)
        {
                int compareResult;
                ListViewItem listviewX, listviewY;

                // Cast the objects to be compared to ListViewItem objects
                listviewX = (ListViewItem)x;
                listviewY = (ListViewItem)y;

                // Compare the two items
                compareResult =
ObjectCompare.Compare(listviewX.SubItems[ColumnToSort].Text,listviewY.SubIte
ms[ColumnToSort].Text);

                // Calculate correct return value based on object comparison
                if (OrderOfSort == SortOrder.Ascending)
                {
                        // Ascending sort is selected, return normal result of compare operation
                        return compareResult;
                }
                else if (OrderOfSort == SortOrder.Descending)
                {
                        // Descending sort is selected, return negative result of compare
operation
                        return (-compareResult);
                }
                else
                {
                        // Return '0' to indicate they are equal
                        return 0;
                }
        }

        /// <summary>
        /// Gets or sets the number of the column to which to apply the sorting
operation (Defaults to '0').
        /// </summary>
        public int SortColumn
        {
                set
                {
                        ColumnToSort = value;
                }
                get
                {
                        return ColumnToSort;
                }
        }

        /// <summary>
        /// Gets or sets the order of sorting to apply (for example, 'Ascending'
or 'Descending').
        /// </summary>
        public SortOrder Order
        {
                set
                {
                        OrderOfSort = value;
                }
                get
                {
                        return OrderOfSort;
                }
        }

I hope this is helpful.

Best regards,

Lion Shi, MCSE, MCSD
Microsoft Support Engineer

This posting is provided "AS IS" with no warranties, and confers no rights.
You assume all risk for your use.  2001 Microsoft Corporation. All rights
reserved.
--------------------

    Subject: how to  sorting listview columns?
    Date: Tue, 26 Mar 2002 09:46:07 +0800
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    if i click a columns,it will be sorted ascending,then i click a same
columns
    again,it will be sorted descending.

This post was very helpful, but I have a follow-up question.  How can
I get the Up/Down icons to draw on the caption bar based on the sort
direction?