With China entering an aging society, the pressure of elderly caring is gradually increasing. As an important pillar of the pension system, the expected demand of annuity should be large, but the actual purchase amount of annuity is far less than expected, which leads to the annuity puzzle. With the help of behavioral economics, this paper analyzes the annuity puzzle. Based on cumulative prospect theory, this paper establishes the criterion of whether investors are willing to buy annuity under discrete time model. Besides, based on the smooth prospect theory, not only the continuous time model of annuity value is constructed, but also the criterion of annuity purchase intention is also established. Numerical simulation and empirical results show that loss aversion is the main reason for the undesirability of annuity, probability distortion further makes annuities unattractive, and risk attitude also affects the value of annuity.