A Rudin-Shapiro photon sieve (RSPS) based on the Rudin-Shapiro (RS) aperiodic sequence is proposed. The RSPS can be fabricated conveniently and generate two images with low chromatic aberration. The plane wave angular spectrum theory is used to study the focusing properties of the RSPSs with different ratios of the diameter of the smallest hole of the sieve to the width of the outermost ring of the corresponding zone plate. The numerical simulation results show that when the ratio is 1.398, the RSPS generates twin foci with the same high intensities in the axial direction. Compared with the RS zone plate (RSZP), the RSPS has more tolerance in the fabrication. It is found that the chromatic aberration generated by RSPS is lower than that by Thue-Morse zone plate (TMZP) and approximately the same as that by RSZP. Hence, the RSPS will have potential applications in the fields of the polychromatic imaging, X-ray microscopy and so on.