create a xml: for ex:mybg.xml
<?xml version="1.0" encoding="utf-8"?>
<selector xmlns:android="http://schemas.android.com/apk/res/android">
<item android:state_pressed="false" android:drawable="@color/anyColor" />
<item android:drawable="@android:color/transparent" />
</selector>
and in your activity xml
do
<Spinner...............
android:drawSelectorOnTop="true"
android:background="@drawable/mybg"/>