My old app is made in Xcode 3.2.6 and now I have purchased a new Mac with Mac OS X version 10.7.3. Now when I'm trying to install Xcode 3.2.6 it completes all the process of installation but after it is done it doesn't create any folder of that SDK and it doesn't show Xcode symbol.
Old Xcode releases are not supported on new OS releases. There are cases where they happen to work, or can be made to work with some expert tweaking, but in the general case developers are much better off migrating their projects to a supported release of the developer tools.
One common misconception many developers have is that they have to use the older tools to support their users on older OSs. This is only true if you are still supporting PowerPC users... in which case you're much better off sticking with PowerPC hardware to produce those builds.
Based on your tags it looks like you are an iOS developer. The latest version of Xcode can still target any version of iOS, IIRC.