A Co∶MgAl2O4 crystal with an initial transmissivity of 89.5% is used as a saturable absorber at a wavelength of 1.3 μm. A low-threshold and high-efficiency passively Q-switched 1319 nm Nd∶YAG laser output is achieved with two-mirror resonator. When the pump power is 10.0 W, a pulsed laser with an average output power of 490 mW, the narrowest pulse width of 18.3 ns, a repetition rate of 17.5 kHz, a pulse energy of 28.1 μJ and a peak power of 1533 W is obtained. The results show that the Co∶MgAl2O4 crytal possesses a good saturable absorption property at a wavelength of 1.3 μm.