Abstract: In order to improve the resolution of far-field diffraction microscopy, a pupil filter whose amplitude transmittance had the distribution of power function with radius was proposed. Theoretical analysis and numerical simulation were carried out. By using scalar diffraction theory, the formula of Fraunhofer diffraction distribution was derived when an amplitude pupil filter with the distribution of power function was added in optical path. Diffraction pattern was obtained through MATLAB software, and the main lobe width of diffraction distribution was compared. The results show that when the power number is 3, Strehl ratio of diffraction distribution is 0.16, the maximum sidelobe intensity ratio is 0.1, the resolution parameter is 0.76, and the enhancement factor of resolution is 1.3. With the increase of power number of amplitude transmittance, the main lobe width decreases. At the same time, the main lobe intensity decreases and the side lobe intensity increases. This study is helpful for the realization of super-resolution imaging in the far field optical microscopes.