The three key drivers of a project success include cost, completion time, and scope, the interplay of which have a significant impact on the decision making in project management. In this study, we propose a theoretical framework to be used as a Project Management Decision Support System for understanding and balancing the interplay between the project cost and quality, which is a key component of the project scope. To this end, we develop a Decision Support Contract (DSC) for a project manager when outsourcing to a contractor whose delivery outcome is subject to quality risk. On the one hand, to reduce the risk of project failure, the contractor can invest in a quality improvement effort, the cost of which is the contractor’s private information. On the other hand, the contractor’s decision on quality improvement is unobservable to the project manager. In designing the DSC, we consider both problems resulting in information asymmetry between the project manager and the contractor. We first obtain the first-best solution assuming that the cost efficiency of the contractor is publicly known, and then solve for the second-best optimal cost plus incentive fee (CPIF) contract under information asymmetry. Our comparative study between the first- and second-best contracts reveals that the project manager may prefer to incur efficiency loss due to underinvestment decision by the high-cost contractor to reduce the information rent demanded by the low-cost contractor. Finally, we compare the effectiveness of CPIF contract to that of fixed-price contract, which enables us to characterize the value of incentive fee term for the project manager. This latter analysis reveals that incentive-fee term is more valuable when the improvement effort is more likely to reduce the quality failure risk.