An evolutionary model was proposed to investigate how the economy can evolve from a system of barter to monetary trade. The replicator equation was employed to describe the process how boundedly rational agents shift their strategies. In doing so, it is found that when the probability of monetary trade is larger than that of barter, the agents change their strategies from rejecting money to accepting money, and an alternative solution to the puzzle that the economy cannot shift from barter equilibrium to monetary one in monetary search model was presented.