The purpose of this paper is to provide the conditions for the convergence of invariant measure obtained from numerical simulations to the exact invariant measure. Santos and Peralta-Alva (2005) have studied the convergence of computed invariant measure of economic models which cannot be solved analytically and must be solved numerically or with some other form of approximation. However, they assume that the state space is compact and therefore, the support of the shock of dynamical system is assumed to be bounded. This paper is to relax the compactness assumption for the convergence of the approximated invariant measure.