Intensity noise spectra of LD pumped Nd:YVO4, Nd:YAG and Nd:YAP single-frequency ring laser are measured experimentally and compared with the spectra calculated with laser quantum model. The results show that there is an intensity noise about tens dB higher than the shot noise level (SNL) at the frequency of several hundred kHz deriving from resonant relaxation oscillation (RRO). In the frequency range of far above RRO, the intensity noise reaches to the SNL. The peak of the RRO shifts to higher frequencies and the height of peak reduces as the pump power increases.