We report a diode end-pumped composite Nd:YAG laser, passively Q-switched by a Cr4+:YAG crystal as saturable absorber. The maximum peak power exceeded 16 kW for an average power of 2.6 W, laser pulses of 16.8-ns duration and 272-muJ energy. The maximum average power was 4.2 W with the laser operating at 24.0 kHz repetition frequency and 47.8-ns pulses duration (3.7 kW peak power) at a beam quality of M-2 = 1.34. A rate-equation model that considers both the active medium and the saturable absorber dynamics was developed. A good agreement between the experiments and modeling resulted.