Recursion relations for orthogonal polynomials, arising in the study of one-matrix model of two-dimensional gravity, are shown to be equivalent to the equations of the Toda-chain hierarchy supplemented by additional Virasoro constraints. This is the case without the double scaling limit. A discrete time variable to the matrix model is introduced. The discrete time dependent partition functions are given by τ functions which satisfy the discrete Toda molecule equation. Further the relations between the matrix model and the discrete time Toda theory are discussed.