Diode-pumped passively Q-switched laser operation of a Nd:GdNbO4 crystal at 1066 nm using Cr4+:YAG as a saturable absorber was demonstrated for the first time. Using two different Cr4+:YAG crystals with initial transmission of 95% and 90% as the saturable absorber for Q-switching, a maximum average output power of 0.50 and 0.41 W was obtained at a pulse repetition frequency of 28.7 and 17.8 KHz, respectively. The shortest pulse width of 23 ns, the largest pulse energy of 22.7 μJ, and the highest peak power of 974.1 W were obtained when the Cr4+:YAG crystal was used with an initial transmission of 90%. The shortest pulse width of 33.3 ns, the largest pulse energy of 17.3 μJ, and the highest peak power of 519 W were obtained when the Cr4+:YAG crystal was used with an initial transmission of 95%. All the results indicate that the Nd:GdNbO4 crystal is a material suitable for diode-pumped passively Q-switched lasers.