Single InAs quantum dot (QD) sample was grown by molecular-beam epitaxy (MBE). The Photoluminescences (PL) of the exciton and biexciton in a single QD were measured at 5 K. The PL intensity as a function of the laser excitation power, the fine structure splittings of the exciton and biexciton, and the corresponding linearly polarized emissions were analyzed. By means of Hanbury-Brown and Twiss (HBT) setup, the photon correlation between the PL of exciton and biexciton were measured, which is gave an evidence of the quantum cascade emissions between biexciton and exciton PL.