The intensity noise properties of the monolithic Nd:YAG nonplanar ring oscillator are investigated via full quantum theory. By theoretical analysis and simulation, it is obtained that the relaxation oscillation is influenced mainly by the vacuum fluctuation, dipole fluctuation and cavity loss. The influence from the pump noise and spontaneous emission noise is relatively small. Meanwhile, the optoelectronic negative feedback of intensity noise is theoretically analyzed, which can provide a theoretical basis for the design of the noise suppression circuit. Based on this theory, the noise suppression circuit is designed which has better phase advance, low noise, wide bandwidth and adequate gain. Experimentally, a satisfied noise suppression result is achieved. For the noise with a relaxation oscillation frequency of 311 kHz, the experimental result shows that the relaxation oscillation noise peak value is reduced about 39 dB, and the intensity noise level is lower than -115 dB/Hz in the entire spectrum.