Also, read the instructions carefully that came with the GFCI receptacle. One set of connections are used for "power-in" and another for "power-out". Depending on where this outlet sits in the circuit, you may have it hooked-up improperly.
When new, the GFCI receptacles usually have a strip of cellophane over the set of connections that feed the rest of the circuit. The set without the cellophane would be used for incoming power.
Generally speaking, a GFCI outlet will protect all downstream items on the same circuit, and will trip if it detects a ground-fault anywhere on the downstream side of the circuit. You may have a ground-fault at another switch or outlet elsewhere on the circuit.