Make sure all your hoses are tight.




If all of those are good, start inspecting the gasket. If its not the gasket, the pump may need to be replaced.



Since its an LSx, and this site is more 3800 oriented, you may find more detailed help or others with your situation on LS1tech.com.
Here's a quick link with people who own LS4s having to replace waterpumps between 25 and 100k mile LS4 water pump problems?? - LS1TECH