Unidirectional single-mode operation of a diode-pumped Nd:YAG laser with a planar semimonolithic ring cavity has been demostrated at 1064 nm. The semimonolithic cavity consists of a laser active medium placed in a magnetic field, a crystal quartz plate, and an output coupling mirror. They form an optical diode by acting each part as a Faraday rotator, a reciprocal polarization rotator and a partial polarizer, respectively. An eigenpolarization theory for the cavity configuration was presented and losses for the eigenmodes were calculated. A pump-limited single-mode output power of 155 mW and a slope efficiency of 17% were obtained when the laser was pumped by a 1.2 W, 809 nm diode-laser. A laser linewidth of less than 100 kHz is inferred from a beat note frequency spectrum between two identical laser systems and continous single-mode tuning range was more than 2 GHz.