In this paper, we combine the design of band-pass frequency selective surfaces (FSSs) with polarization converters to realize a broadband frequency-selective polarization converter (FSPC) with lowbackward scattering, which consists of the top polarization conversion layer backed by a multi-layer bandpass FSS. It is numerically demonstrated that the 1 dB transmission window can be obtained from 8.5 GHz to 11 GHz with a 25.6% fractional bandwidth (FBW), and the bandwidth of reflection below -10 dB is up to 92% from 5.6 GHz to 15.13 GHz. Moreover, the proposed device can achieve two polarization conversion bands (5.66-6.9 GHz and 12.8-15.2GHz) with the polarization conversion ratio over 90%. Besides, by arranging the proposed structure in a checkerboard-like distribution, the backward scattering energy can be reduced in a wide frequency band ranging from 4 to 16 GHz. Both simulation and experimental results are in good agreements, which demonstrates our design strategy. Compared with the conventional polarization conversion designs, the proposed design presents an extra frequency-selective performance and hence can be applied to various practical situations, for instance, working as radomes to transmit the in-band signals with high-efficiency while keeping low-backward scattering for the out-of-band waves.