Quantum computer takes advantages from properties of superposition and entanglement,which are also very fragile and easy to be error. But they may be destroyed easily by a process called decoherence. Therefore,how to overcome the effect of decoherence is key to implement quantum computer. Using the no-jump trajectory,Berry's and AA's formula for geometric phase,we calculate the geometric phase of a spin-1/2 system driven by one and two mode quantum fields subject to decoherence in the adiabatic and nonadiabatic case,respectively. By quantum jump method,we find that the corrections to its phase for the no-jump trajectory are different when considering adiabatic and nonadiabatic evolutions. Finally,we discuss the implications of our results from fundamental and quantum computational points.