How to display transparent activity on the another activity without removing previous activity

declare your activity in manifest like this

 <activity android:name=".yourActivity" android:theme="@android:style/Theme.Translucent.NoTitleBar.Fullscreen"/>

and add a transperent background to your layout like this

 <?xml version="1.0" encoding="utf-8"?>
 <RelativeLayout xmlns:android="http://schemas.android.com/apk/res/android"
android:layout_width="fill_parent"
android:layout_height="fill_parent"
  android:background = "any tranparent image name"  >
 </RelativeLayout>

Edit:

i think you are using this to open your transparent activity it finish your previous activity

Intent intent =new Intent(mContext,yourNewActivity.class);
startActivity(intent);
finish();

remove finish from here then your new activity in on top of previous activity like this

 Intent intent =new Intent(mContext,yourNewActivity.class);
 startActivity(intent);

Hope help..

For the AppCompat style, you can use the following code in your styles.xml, and the add that in your manifest.

styles.xml

<style name="Theme.Transparent" parent="Theme.AppCompat.Light.NoActionBar">
    <item name="android:windowIsTranslucent">true</item>   
    <item name="android:windowBackground">@android:color/transparent</item>
    <item name="android:windowContentOverlay">@null</item>   
    <item name="android:windowNoTitle">true</item>
    <item name="android:backgroundDimEnabled">true</item>
    <item name="colorPrimaryDark">@android:color/transparent</item>
</style>

Manifest

<activity android:name=".HomeActivity"
android:theme="@style/Theme.Transparent" />