On the basis of Becker and Murphy’s theory of rational addiction，this paper makes an extended study． Under the assumption that the life expectancy of addicts is limited，a rational addiction model with finitetime horizon is constructed，and the explicit expressions of optimal addictive consumption and addictive capital are obtained by using the optimal control theory． Studies show that with the increase of life expectancy，rational addicts will reduce their addictive consumption． The addictive consumption is related to the addict’s risk preference and degree of patience and the depreciation rate of addictive capital． The optimal consumption paths demonstrate two typical patterns-monotonically increasing or first slowly decreasing and then rapidly increasing with age． Based on the data of cigarette and alcohol consumption from CHNS，the new model is briefly investigated from an empirical perspective． The study also indicates that in the process of controlling and eliminating harmful addictive behavior，more attention should be paid to the individual characteristics of addicts and addictive goods themselves．