When I plug into GCFI outlet it trips. I tried it into 2 different GCFI outlets on building & same thing happened. When I use extension cord with no ground plug it works fine. Is it a bad plug from ice box?

Is it a bad plug from ice box?

There is a ground fault somewhere, could be plug or could be cord connection to appliance or could be anywhere in appliance.

Assuming ice box is refrigerator..

Ground fault devices are very sensitive and many times where you have electricity and water it will trip the breaker. You need to take an ohm meter and check between the hot prong on plug, which is the smallest one and is on the right top on the receptacle on the wall. If you are reading a high resistance look at wiring and unplug the wires leading to the compressor and see if you still get a reading to ground. If you still get a reading, check the compressor and if it checks out with no reading to ground that is very good. It means that something like the door switch, the fans, light socket, or defrost heater or timer is at fault. Trace it down until you find it so you will not have a fire or electrocute someone.