We reconsider the matrix model formulation of type IIB superstring theory in (9+1)-dimensional space-time. Unlike the previous works in which the Wick rotation was used to make the model well-defined, we regularize the Lorentzian model by introducing infrared cutoffs in both the spatial and temporal directions. Monte Carlo studies reveal that the two cutoffs can be removed in the large-N limit and that the theory thus obtained has no parameters other than one scale parameter. Moreover, we find that three out of nine spatial directions start to expand at some "critical time", after which the space has SO(3) symmetry instead of SO(9).