We present a theoretical investigation of complex dynamical behaviors of an injection-locked semiconductor laser. The Hopf bifurcation which was predicted by the linear stability analysis for the rate equation, has been identified. A period-doubling bifurcation route to chaos and a quasiperiodicity route to chaos have been also identified with the variation of the injection level and the frequency detuning. The boundaries for period-doubling bifurcation, quasiperiodicity and chaos are mapped out in the injection level versus the frequency detuning plane. It was shown that there co-exist two locally stable attractors of limit cycles with period 2. The centers of the attractors shift nonlinearly with the injection level and the frequency detuning. The shift of the center of electric field phase has been estimated by harmonic balance method and compared with those obtained by numerical simulations. The region for bistability is also mapped out.