In the process of project investment decision, the decision maker faces background risks as well as project risks. There often exists a correlation between the background risk and project risk. Therefore, this paper constructs a project investment decision model considering background risks and analyzes the effect of the correlation between the background risk and project risk on investment decision compared with the existing studies. Firstly, the effect of correlation between the additive (multiplicative) background risk and project risk on the investment decision is discussed when the additive (multiplicative) background risk exists alone. Secondly, the investment decision model considering two kinds of the background risks is constructed. Then, the method of monte carlo simulation is used to obtain the results under different degrees of correlation. Based on these, this paper analyzes the impacts of the correlation and correlated degrees between the additive (multiplicative) background risk and project risk on investment decision. Finally, the research conclusions and limitations are summarized.