How to design image for splash screen?

What you describe is what you need to do. You need an image for each screen pixel density group (ldpi, mdpi, hpdi and poss xhdpi)

Other things you can do?

• Use a background around the image so the image appears to stretch (e.g. if image is white near the edges, use a white background). It'll look better if there isn't an obvious border around the image and it fades into a background.
• The background/borders could be a 9-patch, stretchable image
• In theory you could provide a lot more images and select them at runtime based on actual screen size, but it's a very bad idea (you never know what new sizes are coming)
• Remember to include portrait and landscape versions - never a good idea to assume one orientation if you can possibly avoid it

Think of an Android screen like a resizable web page - they come in various different sizes and shapes, and your layout needs to stretch and adapt for all.