We demonstrate a photonic crystal nanocavity laser essentially driven by a self-assembled InAs/GaAs single quantum dot gain and its unique photon statistics. Gain tuning measurements and photon correlation measurements indicated that a single quantum dot plays a substantial role in the laser oscillation. Photon correlation measurements showed a distinct transition from anti-bunching to Poissonian via photon bunching around the threshold with the increase of the excitation power. Numerical simulations, including contributions of other light sources besides a single quantum dot, indicated that the photon bunching feature around the threshold can be enhanced by the interfusion of incoherent photons into the cavity mode.