This work theoretically studies the impacts of the inhomogeneous broadening on the modulation dynamics of quantum dot lasers using a multi-population rate equation model. The modulation dynamics shows two distinct regimes depending on the energy separation between the GS and the ES. For broadenings smaller than the GS-ES separation, the K-factor increases while the damping factor offset, the differential gain and the gain compression factor decrease with the inhomogeneous broadening. For broadenings larger than the GS-ES separation, the damping factor offset keeps almost constant while the K-factor, the differential gain and the gain compression factor increases with the inhomogeneous broadening.