This paper creatively introduces the Markov regime switching model into the defined contribution (DC) pension problem affected by inflation, random interest rate and other factors. It assumes that the parameters in the financial model depend on the market economy state described by the continuous time Markov chain, and obtains the explicit solution of the optimal investment strategy under the Constant Absolute Risk Aversion (CARA) utility function by using the rule of maximizing the expected utility of the wealth of the pension terminal. Finally, the numerical analysis shows that market interest rate, inflation rate and other factors have different degrees of negative impact on the proportion of venture capital investment, and the optimal investment strategy under different economic conditions has significant differences.