Abstract: The purpose of the paper is to study the optimal investment problem with maintenance expenditure of the firm with finite horizon, and to discuss the relationship between the firm's expected return and time and the firm's capital stock. Firstly, applying dynamic programming principle and stochastic analysis, the mathematical model of the company's revenue function is established, which satisfies a parabolic variational inequality with gradient constraint. Then, using the method of partial differential equation, the existence and uniqueness of strong solutions of the parabolic variational inequality are proved by constructing the penalty function, and the corresponding estimates are obtained. The results show that the expected return of the company increases with the increase of the company's capital stock, and decreases with the approaching of the expiration date. It has important theoretical value to guide the design of the optimal investment strategy.