Abstract: This paper is concerned with a kind of problem of maximizing the expected utility from the terminal wealth in the case of inflation. For a class of CRRA utility, we obtain by a direct method an agent's explicit optimal portfolio strategy and the corresponding maximum expected utility. Moreover, we give some economical interpretations. This idea comes from the completion-of-square technique of linear quadratic optimal control problems. In Section 3, based on the history data of the stock price and the inflation rate, the values of the parameters in models are estimated with SAS software. And then, the explicit optimal portfolio strategy and the maximum expected utility are also given.