The rate equations of self-assembled quantum dot laser are solved by using fourth order Rung-Kutta method and with considering effects of homogeneous and inhomogeneous broadening of optical gain, static and dynamic characteristics of this laser are investigated. Results are showed with increasing of different between homogeneous and inhomogeneous broadening, degradation of statics characteristics, nonlinearity in light-current characteristics and decreasing of slop-efficiency are appeared. Increasing of current injection is caused the dynamic characteristics, relaxation oscillation frequency, modulation bandwidth and turn on delay are heightened. In addition threshold current and turn on delay decrease with increasing of homogeneous broadening.