Based on the instability criterion of semi-classical Maxwell-Bloch equations of single-mode laser with an injected signal, we investigated the instability of this system In. particular, we examined the global structure of Hopf instabiliy domain in the entire parameter space and derived the boundary of this domain analytically. We also found a full hysteresis loop between the bistable states of the output laser intensity in the active cavity case and discussed the condition of occurance of such phenomenon.