With Cr4+:YAG as a saturable absorber, a passively Q-switched self-frequency-doubled (SFD) laser based on a trigonal Nd:Ca3NbGa3Si2O14 (Nd:CNGS) silicate crystal was demonstrated for the first time. The maximum average output power at 532 nm was 16.2 mW, and the corresponding pulse repetition frequency, single pulse energy, pulse duration and peak power were 2.25 kHz, 7.2 μJ, 13.7 ns, 0.53 kW, respectively. We also present a rate-equation model of such a passively Q-switched SFD laser showing a good agreement with the experiment. Nd:CNGS is a promising pulse SFD material for miniature all-solid-state visible light sources.