Hi,

You Can Remove one Section from thsi then only Vertical bar will be displayed... I made alittle change here... 

<Application.Resources>

<Style x:Key="ScrollViewerStyle1" TargetType="ScrollViewer">

<Setter Property="IsEnabled" Value="true"/>

<Setter Property="Foreground" Value="#FF000000"/>

<Setter Property="BorderBrush" Value="#FFA4A4A4"/>

<Setter Property="BorderThickness" Value="1"/>

<Setter Property="HorizontalContentAlignment" Value="Left"/>

<Setter Property="VerticalContentAlignment" Value="Top"/>

<Setter Property="Cursor" Value="Arrow"/>

<Setter Property="TextAlignment" Value="Left"/>

<Setter Property="TextWrapping" Value="NoWrap"/>

<Setter Property="FontSize" Value="11"/>

<Setter Property="VerticalScrollBarVisibility" Value="Visible"/>

<Setter Property="Template">

<Setter.Value>

<ControlTemplate TargetType="ScrollViewer">

<Border BorderBrush="{TemplateBinding BorderBrush}" BorderThickness="{TemplateBinding BorderThickness}" CornerRadius="1">

<Grid Background="{TemplateBinding Background}">

<Grid.RowDefinitions>

<RowDefinition Height="*"/>

<RowDefinition Height="Auto"/>

</Grid.RowDefinitions>

<Grid.ColumnDefinitions>

<ColumnDefinition Width="*"/>

<ColumnDefinition Width="Auto"/>

</Grid.ColumnDefinitions>

<Rectangle Grid.Column="1" Grid.Row="1" Fill="#FFE9E9E9"/>

<ScrollContentPresenter Cursor="{TemplateBinding Cursor}" Margin="{TemplateBinding Padding}" x:Name="ScrollContentPresenter" Background="{TemplateBinding Background}" HorizontalContentAlignment="{TemplateBinding HorizontalContentAlignment}" VerticalContentAlignment="{TemplateBinding VerticalContentAlignment}" Grid.Column="0" Grid.Row="0" Content="{TemplateBinding Content}" ContentTemplate="{TemplateBinding ContentTemplate}" TextAlignment="{TemplateBinding TextAlignment}" TextDecorations="{TemplateBinding TextDecorations}" TextWrapping="{TemplateBinding TextWrapping}"/>

<ScrollBar Cursor="Arrow" HorizontalAlignment="Left" Margin="0,0,0,0" x:Name="VerticalScrollBar" Width="18" Visibility="{TemplateBinding ComputedVerticalScrollBarVisibility}" Grid.Row="0" Orientation="Vertical" ViewportSize="{TemplateBinding ViewportHeight}" Maximum="{TemplateBinding ScrollableHeight}" Minimum="0" Value="{TemplateBinding VerticalOffset}" d:LayoutOverrides="Width"/>

</Grid>

</Border>

</ControlTemplate>

</Setter.Value>

</Setter>

</Style>

</Application.Resources>

///Paste this in Your Page.Xaml...

<UserControl x:Class="ListBoxSample.Page"

Width="400" Height="300" xmlns:d="http://schemas.microsoft.com/expression/blend/2008" xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006" mc:Ignorable="d">

<UserControl.Resources>

<Style x:Key="TextBoxStyle1" TargetType="TextBox">

<Setter Property="Template">

<Setter.Value>

<ControlTemplate TargetType="TextBox">

<Grid x:Name="RootElement">

<Grid.Resources>

<Storyboard x:Key="Normal State">

<DoubleAnimationUsingKeyFrames Storyboard.TargetName="FocusVisualElement" Storyboard.TargetProperty="(UIElement.Opacity)">

<SplineDoubleKeyFrame KeyTime="00:00:00" Value="0"/>

</DoubleAnimationUsingKeyFrames>

</Storyboard>

<Storyboard x:Key="Focused State">

<DoubleAnimationUsingKeyFrames Storyboard.TargetName="FocusVisualElement" Storyboard.TargetProperty="(UIElement.Opacity)">

<SplineDoubleKeyFrame KeyTime="00:00:00" Value="1"/>

</DoubleAnimationUsingKeyFrames>

</Storyboard>

</Grid.Resources>

<ScrollViewer x:Name="ContentElement" Style="{StaticResource ScrollViewerStyle1}"/>

<Rectangle x:Name="FocusVisualElement" IsHitTestVisible="False" Opacity="0" StrokeThickness="2" RadiusX="1" RadiusY="1" VerticalAlignment="Stretch" Margin="0,0,0,0">

<Rectangle.Stroke>

<LinearGradientBrush EndPoint="0.5,1" StartPoint="0.5,0">

<GradientStop Color="#FFA9B9C5" Offset="0"/>

<GradientStop Color="#FF668499" Offset="0.325"/>

<GradientStop Color="#FF244E6D" Offset="0.325"/>

<GradientStop Color="#FF4F7189" Offset="1"/>

</LinearGradientBrush>

</Rectangle.Stroke>

</Rectangle>

</Grid>

</ControlTemplate>

</Setter.Value>

</Setter>

</Style>

</UserControl.Resources>

<Grid x:Name="LayoutRoot" Background="White">

</UserControl>