排序是根据列的类型来的，就ID列来说，int类型的排序结果是3，5，17，而如果你把该列类型改为string，结果就会是17,3,5，如果你定义列的时候不加类型，默认是string，如果是自定义类型，那么请继承IComparable接口，实现CompareTo方法。

XAML

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<Window x:Class="ListViewSort.Window1"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    Title="Window1" Height="300" Width="300" Loaded="Window_Loaded">
    <Grid>
        <ListView x:Name="lv" GridViewColumnHeader.Click="GridViewColumnHeader_Click"  IsSynchronizedWithCurrentItem="True" ItemsSource="{Binding}" Margin="0,0,0,70">
            <ListView.View>
                <GridView>
                    <GridViewColumn  Header="ID" DisplayMemberBinding="{Binding ID}" />
                    <GridViewColumn  Header="Name" DisplayMemberBinding="{Binding Name}" />
                </GridView>
            </ListView.View>
        </ListView>
    </Grid>
</Window>
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C#

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using System;
using System.Collections.Generic;
using System.Text;
using System.Windows;
using System.Windows.Controls;
using System.Windows.Data;
using System.Windows.Documents;
using System.Windows.Input;
using System.Windows.Media;
using System.Windows.Media.Imaging;
using System.Windows.Navigation;
using System.Windows.Shapes;
using System.Data;
using System.ComponentModel;

namespace ListViewSort
{
    /// <summary>
    /// Interaction logic for Window1.xaml
    /// </summary>
    public partial class Window1 : Window
    {
        public Window1()
        {
            InitializeComponent();
        }

        private void Window_Loaded(object sender, RoutedEventArgs e)
        {
            //Initialize datasource
            DataTable dt = new DataTable();
            dt.Columns.Add("ID", typeof(Int32));
            dt.Columns.Add("Name", typeof(string));
            dt.Rows.Add(5, "Apple");
            dt.Rows.Add(17, "Orange");
            dt.Rows.Add(3, "Banana");

            lv.DataContext = dt;
        }

        private void GridViewColumnHeader_Click(object sender, RoutedEventArgs e)
        {
            if (e.OriginalSource is GridViewColumnHeader)
            {
                //Get clicked column
                GridViewColumn clickedColumn = (e.OriginalSource as GridViewColumnHeader).Column;
                if (clickedColumn != null)
                {
                    //Get binding property of clicked column
                    string bindingProperty = (clickedColumn.DisplayMemberBinding as Binding).Path.Path;
                    SortDescriptionCollection sdc = lv.Items.SortDescriptions;
                    ListSortDirection sortDirection = ListSortDirection.Ascending;
                    if (sdc.Count > 0)
                    {
                        SortDescription sd = sdc[0];
                        sortDirection = (ListSortDirection)((((int)sd.Direction) + 1) % 2);
                        sdc.Clear();
                    }
                    sdc.Add(new SortDescription(bindingProperty, sortDirection));
                }
            }
        }
    }
}
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