The linewidth enhanment factor is one of the key parameters for semiconductor lasers. The value of linewidth enhanment factor is different in kinds of type semiconductor lasers. The dependency of the nonlinear period-one oscillation in optically injected semiconductor on the linewidth enhanment factor was numerically investigated, with the single-mode rate-equation of optical injection semiconductor laser. The results show that linewidth enhancement factor strongly affect the dynamical behavior of the system. As the linewidth enhancement factor increases, the range of the period-one oscillation and its frequency increase, and the injection locking stable state is suppressed greatly. Moreover, the optical spectrum and frequency of the period-one oscillation were investigated. The results reveal that the frequency of the period-one oscillation increases as the linewidth enhancement factor, injection strength and frequency detuning increasing.