There is only one partition in my hard disk. I want to give a partiton on it. Is there any way to resize it without using any live cd?
depends on the underlying filesystem BUT in most cases its NOT recommended to do this anyway - except you are using a LVM which is designed to do this.
With only one partition its sure that this one is the root partition and that is used (mounted) when your system runs...
WHY don't you want to use a live cd?