Using vector diffraction theory, the superresolution properties of Gaussian beam are studied under high numerical aperture. The two and three rings phase structures, which can realize superresolution, are solved and optimized. The varirty regularities of superresolution properities are analyzed with the changing of radius and phase. The methods and solutions of optimization are also given. The results show that superresolution can be get with the same side lobe at illumination of plane wave, when using the Gaussion beam illumination.The inner radius is crucial when using two ring phase structure and the property of superresolution has little change with tiny phase changing. Two ring phase structures have the advantages of machining tolerances. Three ring phase structures can get larger compression radio and small peak intensity of the main lobe with the same side lobe. The changing of radius and phase has important influence on the performance of superresolution. The machining tolerance is smaller than that of two ring phase structure. For both two and three ring phase structure, the increase of compression radio will inevitably cause the decrease of main lobe peak intensity and the increasing of the sidelobe radio. This research provides a new method for the design of superresolution pupil filter with Gaussian beam illumination under high numerical aperture.