A passively Q-switched self-frequency doubling (SFD) green laser based on quasi-continuous diode-pumped and Nd:Ca3TaGa3Si2O14 crystal was developed for the first time with Cr4+:Y3Al5O12 as the saturation absorber. The output wavelength was 533 nm and the maximum average output power was 57 mW, corresponding to single pulse energy, pulse duration, and peak power of 190 μJ, 14.35 ns, and 13.24 kW, respectively. To our knowledge, this is the best result of diode-pumped, pulsed SFD lasers to date. Its compact components and low cost provide a better way to obtain an all-solid-state, miniaturized green laser with high peak power.