In this paper we consider the pure exchange overlapping-generations model with money. This model assumes the double infinity of consumers and commodities. Hence it is not so easy to show the existence of a competitive equilibrium in this model as to show a competitive equilibrium in the finite horizon economy. This paper claims to prove the existence theorem: Under a set of assumptions about consumer's utility functions and initial endowments, we show the existence of a monetary competitive equilibrium where money has a finite positive exchange value over the infinite horizon.