We demonstrate numerical analysis of the dynamics and noise of semiconductor laser (SL) with optical feedback (OFB) and nonlinear gain (NLG). The simulations are based on an improved time-delay rate equations model that takes into account the multiple round-trips of the lasing field in the external cavity. The temporal trajectory of the photon number, bifurcation diagrams, and relative intensity noise (RIN) is used to perform this analysis. The results show that when NLG included the Hopf bifurcation point moved towards the direction of increasing OFB strength. Period doubling, or sub-harmonics operation, is the route to chaos of SL depending on whether NLG is included or not. In the periodic oscillation (PO) and route to chaos regimes, including the NLG causes a significant frequency shift relative to the frequency in the case without NLG. Under strong OFB, the inclusion of NLG changes chaotic dynamics to continuous wave operation or PO depending on the OFB strength and characterized by RIN near to or higher than the RIN of the solitary laser. At high-frequency regime, the RIN is characterized by the compound cavity frequency or the external cavity frequency depending on the NLG whether included or not.