A Q-band two-beam cryogenic receiver for the Tianma Radio Telescope (TMRT) has been developed, and it uses the independently-developed key microwave and millimeter-wave components operating from 35 to 50GHz with a fractional bandwidth of 35%. The Q-band receiver consists of three parts: optics, cold unit assembly and warm unit assembly, and it can receive simultaneously the left-handed and right-handed circularly polarized waves. The cold unit assembly of each beam is composed of a feed horn, a noise injection coupler, a differential phase shifter, an orthomode transducer and two low-noise amplifiers, and it works at a temperature range near 20K to greatly improve the detection sensitivity of the receiving system. The warm unit assembly includes four radio-frequency amplifiers, four radio-frequency high-pass filters, four waveguide biased mixers, four 4-12GHz intermediate-frequency amplifiers and one 31-38GHz frequency synthesizer. The measured Q-band four-channel receiver noise temperatures are roughly 30-40K. In addition, the single-dish spectral line and international very long baseline interferometry (VLBI) observations between the TMRT and East Asia VLBI Network at the Q-band have been successfully carried out, demonstrating the advantages of the TMRT equipped with the state-of-the-art Q-band receiver.