How to add border around linear layout except at the bottom?

Create an XML file named border.xml in the drawable folder and put the following code in it.

 <?xml version="1.0" encoding="utf-8"?>
 <layer-list xmlns:android="http://schemas.android.com/apk/res/android">
  <item> 
    <shape android:shape="rectangle">
      <solid android:color="#FF0000" /> 
    </shape>
  </item>   
    <item android:left="5dp" android:right="5dp"  android:top="5dp" >  
     <shape android:shape="rectangle"> 
      <solid android:color="#000000" />
    </shape>
   </item>    
 </layer-list> 

Then add a background to your linear layout like this:

         android:background="@drawable/border"

EDIT :

This XML was tested with a galaxy s running GingerBread 2.3.3 and ran perfectly as shown in image below:

ALSO

tested with galaxy s 3 running JellyBean 4.1.2 and ran perfectly as shown in image below :

Finally its works perfectly with all APIs

EDIT 2 :

It can also be done using a stroke to keep the background as transparent while still keeping a border except at the bottom with the following code.

<?xml version="1.0" encoding="utf-8"?>
 <layer-list xmlns:android="http://schemas.android.com/apk/res/android">
   <item android:left="0dp" android:right="0dp"  android:top="0dp"  
        android:bottom="-10dp"> 
    <shape android:shape="rectangle">
     <stroke android:width="10dp" android:color="#B22222" />
    </shape>
   </item>  
 </layer-list> 

hope this help .

Save this xml and add as a background for the linear layout....

<shape xmlns:android="http://schemas.android.com/apk/res/android"> 
    <stroke android:width="4dp" android:color="#FF00FF00" /> 
    <solid android:color="#ffffff" /> 
    <padding android:left="7dp" android:top="7dp" 
            android:right="7dp" android:bottom="0dp" /> 
    <corners android:radius="4dp" /> 
</shape>

Hope this helps! :)