Hi Sandeep,
Whichever user that you are using to assign the package privilege must have access to that package in order to grant it to somebody else. You said you are using SYSTEM user. If you look at package privileges tab for the SYSTEM user do they either have a) Root Package or b) your new package name explicitly listed? Then on the very right-hand side under 'Privileges for native packages' do they have option 'grantable to others'? Without this they can not grant for this new user.
-Patrick