In this paper, we study a two-dimensional lease contract with preventive maintenance and servicing strategy involving imperfect repair. The lease contract coverage is characterized by two parameters – age and usage. The lessor will carry out preventive maintenance (PM) and a servicing strategy which allows more than one imperfect repairs under the contract. In the lease contract studied, we consider that a penalty cost incurred when the time required to perform an imperfect repair exceeds a target. This servicing strategy aims to reduce equipment failures and hence decreasing the penalty cost and maintenance cost during the leased contract. We find the optimal PM degree and the imperfect repair strategy such that the expected total cost is minimized. Numerical examples are presented to illustrate the optimal PM and servicing strategy for various usage rates (heavy, moderate and low usage rates), and compared results for this servicing strategy with those of minimal repair strategy