우선 drawable 리소스에 가서 이런 xml을 만들어줍니다.

<?xml version="1.0" encoding="utf-8"?>
<!--  res/drawable/rounded_edittext.xml -->
<shape xmlns:android="http://schemas.android.com/apk/res/android"
android:shape="rectangle" android:padding="10dp">
 <solid android:color="#FFFFFF"/>
    <corners
     android:bottomRightRadius="15dp"
     android:bottomLeftRadius="15dp"
  android:topLeftRadius="15dp"
  android:topRightRadius="15dp"/>
</shape>

그리고 EditText의 background에 해당 drawable을 적용해줍니다.

<?xml version="1.0" encoding="utf-8"?>
<LinearLayout xmlns:android="http://schemas.android.com/apk/res/android"
    android:orientation="vertical"
    android:layout_width="fill_parent"
    android:layout_height="fill_parent"
    >
<EditText  
    android:layout_width="fill_parent" 
    android:layout_height="wrap_content" 
    android:padding="5dip"
    android:background="@drawable/rounded_edittext" />
</LinearLayout>