The paper extends the classical Merton model by incorporating the agent’s over-extrapolation bias to investigate its effects on investment，consumption decisions and the corresponding welfare． By using the standard dynamic programming and controlling method，and Kalman filtering，the semi-closed form solutions are obtained for the scaled certainty equivalent wealth，the financial investment，and the consumption strate-gies based on the CＲＲA utility function． The numerical analysis with calibrated parameters shows that over-ex-trapolation will induce under-investment and over-consumption and increase the marginal propensity to con-sume significantly． Finally，the theoretical model predicts that 10% of the over-extrapolation bias will result in a 30% loss of welfare．