This paper extends the discrete time sentiment asset pricing model to the continuous time setting using the consumption based pricing model. By incorporating heterogeneity in Lucas’s pure exchange economy, a dynamic sentiment asset pricing model for heterogeneous investors is established, and a central planning problem is studied. The investors’ subjective drift rate of the stock price is derived by considering the sentiment factors, and then used in a dynamic asset pricing problem for heterogeneous investors to portray the differences between rational investors and sentiment investors. Contrary to the conventional wisdom that equilibrium stock price is not affected by investors’ sentiment, this paper finds that investors’ sentiment has a significant impact on the equilibrium stock price. Numerical examples and sensitivity analyses show that false expectation will lead to an increase in the drift rate of the stock price.