We investigate the influence of non-glide stresses on the Peierls energy of screw dislocation by using Nudged-Elastic-Band method. The influence of the applied non-glide stress fields on the Peierls energy of a screw dislocation is clearly observed. Moreover, we find that the stress field dependence of the Peierls energy is changed by the moving direction of the screw dislocation under a specific applied stress field. Geometrical parameters, which can measure the atomic elastic deformation around the screw dislocation core, are introduced to explain the stress field dependence of the Peierls energy. Finally, the cross slip of a screw dislocation around a precipitate with a misfit strain is discussed by combining the analytical solution of stress fields around the precipitate with the geometrical parameters obtained by our atomic simulations.