Time dependence of the photoluminescence (PL) attributed to the exciton and biexciton in a single $\mathrm{In}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ quantum dot is investigated at $4.3\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ with microscopic spectroscopy. Dynamical behavior of the PL decay and the excitation intensity dependence of the exciton and biexciton PL are analyzed by rate equations assuming a cascading recombination from the biexciton to exciton state. The analysis shows that the biexciton lifetime is longer than the exciton lifetime. The estimated ratio of the biexciton lifetime to the exciton lifetime shows a molecular nature of the biexciton in the large quantum dots compared with the exciton Bohr radius.