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 50 GHz 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-hand and right-hand 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 20 K temperature zone 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 4-12 GHz intermediate-frequency amplifiers and one 31-38 GHz frequency synthesizer. The measured Q-band four-channel receiver noise temperatures are roughly 30-40 K. In addition, the single-dish spectral line and international very long baseline interferometry (VLBI) observations between the TMRT and East Asia VLBI Network at Q-band have been successfully carried out, demonstrating the advantages of the TMRT equipped with the state-of-the-art Q-band receiver. In addition, the facility of our microwave technology lab will be briefly introduced.