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Question:
I will add a image to show it. <a href="https://drive.google.com/file/d/0B-dRDlHZAgYbVG5Ca1l2MTZseHc/edit?usp=sharing" rel="nofollow">https://drive.google.com/file/d/0B-dRDlHZAgYbVG5Ca1l2MTZseHc/edit?usp=sharing</a> you can see the detail in the image.
Answer1:For each grid item use the background below :-<br /> (save the below code in drawable folder)
<layer-list xmlns:android="http://schemas.android.com/apk/res/android">
<item android:bottom="1dp" android:left="1dp" android:right="1dp" android:top="1dp">
<shape android:shape="rectangle">
<solid android:color="@color/black_transparent"/>
<corners android:bottomRightRadius="12dp" android:bottomLeftRadius="12dp" android:topLeftRadius="12dp" android:topRightRadius="12dp"/>
</shape>
</item>
</layer-list>
Answer2:make grid_item_corner.xml in drawable folder.
<?xml version="1.0" encoding="utf-8"?>
<layer-list xmlns:android="http://schemas.android.com/apk/res/android">
<item
android:bottom="1dp"
android:left="1dp"
android:right="1dp"
android:top="1dp">
<shape android:shape="rectangle">
<solid android:color="@android:color/transparent" />
<corners
android:bottomRightRadius="10dp"
android:bottomLeftRadius="10dp"
android:topLeftRadius="10dp"
android:topRightRadius="10dp" />
</shape>
</item>
</layer-list>
and set grid <strong>single layout</strong> item
android:background="@drawable/grid_item_corner"
I hope this will help you.
Note: Above background property is about grid view single item layout, not to gridview.