In this research we have solved the rate equations for InAs/AlGaAs broadband selfassembled quantum dot (QD) laser with considering the homogeneous broadening (HB) and inhomogeneous broadening (IHB) of the linear optical gain using fourth order Runge-Kutta method. We show that enhancing the injected current results in improving the dynamic characteristics, and increasing the steady-state photons, and show that with increase of the full width at half maximum (FWHM) of HB, the threshold current, turn-on delay and steady-state photons increase. Our calculation results also show that the simulated broadband selfassembled QD laser does not reach the complete steady-state when HB is near or equal to IHB.