The ability of geometric quantum gate against the fluctuations of control external field was researched. We replace the random fluctuations by the periodic perturbation. In this approximation,the result shows that no matter the Berry geometry phase or the AharonovAnandan(A-A)geometry phase has the same ability against the stochastic fluctuations as their corresponding dynamics phases. And numerical results also justify that the Berry phase is more powerful to resist the external field fluctuation than that of the A-A phase. We believe that this distinction is caused by adiabatic approximation purely. Lastly,it is validated that the geometry quantum gates constructed by an orthogonal state scheme are more powerful against the fluctuations.