We introduce small-signal modelling on both relative intensity noise (RIN) and frequency noise (FN) as well as the associated linewidth of the semiconductor laser. Influence of gain suppression on the frequency characteristics of the RIN and FN spectra and the corresponding damping rate and frequency of relaxation oscillations are elucidated. Also, we investigate the dependence of laser noise on the mathematical form of nonlinear gain using three common formulas of optical gain over a wide range of injection current. We show variations of the levels of both RIN and FN with the form of optical gain in the regime of resonance frequency as a result of variation of damping rate and resonance frequency. The tolerances in predicting the RIN and FN levels are 1% and 14%, respectively, which corresponds to the tolerance of linewidth of 21.6% at low frequency of 10 MHz and current of five times its threshold value, while they are 39% and 21.6% at the relaxation frequency.