Computational lithography is an effective way to improve the lithographic imaging performance. However, most computational lithography technologies are usually established in an ideal lithography system without considering the impact of system errors. In fact, the stage vibration among the system errors can increase the lithographic pattern error and decrease the process window(PW). Therefore, it is imperative to reduce the impact of stage vibration on lithographic performance. For the first time to our knowledge, a lithography system holistic optimization method with low stage vibration sensitivity was proposed. Firstly, the source was represented by Zernike polynomials for easing the computational burden and improving the source flexibility. Then a weighted cost function incorporating the influence of stage vibration which consists of critical dimension error(CDE) and depth of focus(DOF) was built. Finally, a gradient-based statistical optimization algorithm was applied to build the optimization framework. The simulations of 1D mask pattern at 14 nm node show that for the system with extreme stage vibration, compared with the traditional method, the CDE of the proposed method is reduced by 28.7%, and the PW is increased by 67.3%. The results demonstrate that this method reduces the vibration sensitivity and improves the process robustness effectively.