Low noise all-solid-state single-frequency Nd:YVO4 lasers are important for applications in quantum precision measurement, atomic frequency standard, non-classical state preparation and gravitational wave detection. The laser’s intensity noise has become a crucial parameter since it can directly affect measurement accuracy or experimental results. By altering laser parameters such as the intensity noise of the pump, intracavity losses, and the transmissionof output coupler, the intensity noise of the all-solid-state single-frequency Nd:YVO4 laser is fully investigated. The intensity noise can only be slightly improved by optimizing these parameters. The main factor affecting noise level is relaxation oscillation, thus changing the state of relaxation oscillation is an efficient method for reducing the intensity noise. By altering the gain and phase of the noise transfer function, the photoelectronic negative feedback technique can effectively suppress the intensity noise. The intensity noise is reduced by about 5 dB in the audio frequency region and by about 36 dB at the relaxation oscillation frequency with the support of reflectivity of beam splitter ε=10%, DC gain g=15xtdB, the amount of phase advance φ=60° and the pump noise VP=15dB. By using a low noise injection field, the injection locking technology can modify the relaxation oscillation’s state and effectively suppress the noise in the relaxation oscillation frequency region. The maximum intensity noise is decreased by around 31 dB with the help of injection laser noise Vin=5dB, injection locking power amplification ratio H=50 and the pump noise VP=15dB. The photoelectric negative feedback technique may reduce noise in both the audio frequency region and the relaxation oscillation frequency region, the injection locking technique can only do so in the relaxation oscillation frequency region. The noise in the relaxation oscillation zone can be suppressed more strongly by combining the two techniques. The intensity noise of the all-solid-state single-frequency Nd:YVO4 laser is reduced by about 5 dB in the audio frequency region andby about 39 dB around the peak of the relaxation oscillation with the feasible parameters of ε=10%, g=15dB, φ=60°, H=20 and the real injection laser noise. The theoretical analysis in this paper will aid in the creation of an all-solid-state low noise Nd:YVO4 laser.