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The theoretical analysis of optical gain and chirp characteristics of a semiconductor quantum dot (Qdot) broadband laser is presented. The model based on population rate equations, has been developed to investigate the multiple states lasing or quasi-supercontinuum lasing in InGaAs/GaAs Qdot laser. The model takes into account factors such as Qdot size fluctuation, finite carrier lifetime in each confined energy states, wetting layer induced nonconfined states and the presence of continuum states. Hence, calculation of the linewidth enhancement factor together with the variation of optical gain and index change across the spectrum of interest becomes critical to yield a basic understanding on the limitation of this new class of lasers. Such findings are important for the design of a practical single broadband laser diode for applications in low coherence interferometry sensing and optical fiber communications. Calculation results show that the linewidth enhancement factor from the ground state of broadband Qdot lasers ( alpha ~ 3) is slightly larger but in the same order of magnitude as compared to that of conventional Qdot lasers. The gain spectrum of the quasi-supercontinuum lasing system exhibits almost twice the bandwidth than conventional lasers but with comparable material differential gain ( ~ 10-16 cm2) and material differential refractive index ( ~ 10-20 cm3) near current threshold.