There are three types of superresolving pupil filters in the optical systems, namely, amplitude type, phase-only type and amplitude-phase type. Among them, phase-only filter has received more attention because of its higher diffractive efficiency than others. The superresolving continuous phase filters were reported in Optics Letters in 2003 by Daniel M. de Juana et al. In this work, a new type of phase-only superresolving pupil filters, varying in discretely continuous way, is presented, whose phase distribution includes two parts: the first part is a sine function, that is, a continuous phase profile; the second part is a constant term, which can be different in the different range of the filter. The goal of the research is to find better results than the superresolving continuous phase filters. From the numerical results, we can see that this type filters can provide higher superresolving performance than the continuous phase filters. This filter with discrete continuous phase zones is also useful for analyzing the performance of a discrete phase filter illuminated with a continuous wavefront. Therefore, although this phase-only superresolving pupil filters are difficult to fabricate at present, the research on this type pupil has an important meaning both in theory and application.