Reinstall Oracle 11G2 Running Oracle 11GR2 instance (non-ASM). Plan to set it up again from the scratch(this time using ASM, Grid infrastructure). And I need the present database.

I am thinking of the simple plan:
1) Backup using RMAN the existing instance.
2) Deinstall the existing instance.
3) Install Grid.
4) Install Oracle DB software. (Same version)
5) Restore RMAN backup.

Is this how I should proceed, or is there any other plan of action I can look to.

Thanks
The Oracle docs for 11.2 ASM migration are here:

http://docs.oracle.com/cd/E11882_01/server.112/e18951/asm_rman.htm#OSTMG12000

These explain the process that you need to go through to migrate to ASM from filesystem storage.