A planar millimeter-wave third-harmonic mixer with low conversion loss is proposed. The mixing circuit consists of a substrate-integrated waveguide (SIW) balun, a pair of diodes, a diplexer and microstrip matching circuit. The mixer is ideal for use as down-converter and up-converter. For a fixed intermediate frequency (IF) of 2 GHz, the mixer has an up-conversion loss of 14.5-15.6 dB and a down-conversion loss of 14-15.6 dB over the radio frequency (RF) band of 38-47 GHz. For a fixed local oscillation (LO) frequency of 13 GHz, the mixer has a conversion loss of 10-15.8 dB over the IF frequency band of DC-6.4 GHz. The proposed mixer offers an effective and low-cost solution for millimeter-wave applications.