I am creating an application that write some data to the database. For checking I need to open the database in applications.

I think it should be in

~/Library/Application Support/iphone simulator....

I have not found the iphone simulator folder in Application Support.I have installed ios 4.2, and simulator is working properly.

Where can I find it?

Xcode versions 3.x-5.x

Simulator usually is installed together with SDK so most probably you should look (e.g., if you installed Xcode 3.1 and SDK 4.3 in their default locations) within:

/Developer/Platforms/iPhoneSimulator.platform/Developer/Applications/iOS Simulator.app

Apps that are installed on your iPhone Simulator should be (if for example compiled for iOS 4.3) located in:

~/Library/Application Support/iPhone Simulator/4.3/Applications/[app GUID]

If you are looking for .sqlite database within Application, it should reside in:

~/Library/Application Support/iPhone Simulator/4.3/Applications/[app GUID]/Documents/[appname].sqlite 

Xcode 6

The simulator devices are located in:

~/Library/Developer/CoreSimulator/Devices/

so your application data (e.g. application database in app Document folder) will be in

~/Library/Developer/CoreSimulator/Devices/[simulator device id]/data/Applications/[app GUID]/Documents/[appname.sqlite]

On Mac OS X 10.7 the users/[username]/Library is hidden. Reveal it using:

chflags nohidden ~/Library