Campbell and Viceira (2001) were the first to incorporate inflation risk into the optimal portfolio problem and found that the investor decreased the holding weights of long term bonds in the absence of inflation-linked underlying assets. Xia (2001) found that opportunity cost was significantly substantial when investors ignored the learning mechanism of uncertainty parameters and used the learning method to predict the parameter of the dynamics of stock price. In this study, we not only show that the learning process increases the utility value of terminal wealth, but also analyze the effect of learning process on the expected utility value of terminal wealth. The results are as follows. 1. Investment horizon, instantaneous volatility of inflation rate and risk attitude positively affects the learning process on the terminal wealth and its expected utility. The effects are more significant when the investment horizon, volatility and risk-averse attitude increase. 2. When volatility of the consumer price index and the estimation error increase, the learning ability enhance the expected wealth and utility. However, the improvement rate of utility decrease since investors becomes hardly learn from the inflation rate.