In order to study far-field optical imaging system with continuous phase optical pupil filter and to achieve the purpose of high resolution in this system, a phase optical pupil filter with polynomial function is proposed. With this filter, three-dimensional super-resolution can be obtained in optical system. The contrast with the effects on super-resolution of a typical three-zone phase optical pupil filter is shown in the following. There is a significant improvement on transverse resolution with the new type filter, but the Strehl ratio will decline. In addition, more adjustable parameters can be established to restrain such a filter by increasing the highest power of the polynomial function, which makes the filter more flexible in improving the resolution of optical system. The numerical results about the continuous-phase optical pupil filter with polynomial functions will also help the manufacture.