We present a theoretical investigation of complex dynamical behaviors of an injection-locked semiconductor laser. A period-doubling bifurcation route to chaos and bistability has been identified. The boundaries for period-doubling bifurcations and chaos are mapped out in the injection-level-frequency-detuning plane. It was shown that there exist two locally stable attractors of limit cycles. The centers of the attractors shift nonlinearly with injection level. The shift of the center of the electric-field phase is estimated by the harmonic balance method.