There's a spring that holds the grip safety bar forwards against the back of the trigger. This works with a protrusion on the grip safety. When the safety is engaged (no grip), the trigger pushes this bar backwards and it hits the grip safety protrusion, stopping the trigger. Disengaging the safety (gripping the gun) pulls the protrusion upwards, out of the way of the protrusion, and the bar slides backwards into the grip safety when you pull the trigger.
Some things that come to mind.
- Grip safety isn't installed right or is defective. It might not be pulling the protrusion fully out of the way of the bar.
- Spring could be weak. If the spring is weak (or non-existent/destroyed) the bar might be in contact with the safety even when the trigger isn't being pulled, and gripping the safety could 'drag' the bar upwards with the protrusion.
Really the only way to tell is for you to take the grips off and see what is (or could be) going wrong.