This paper describes the development of a constraint programming (CP) model for schedule optimization to satisfy both deadline and resource constraints in large-scale construction projects. Unlike many meta-heuristic methods in the literature, the CP model is fast and provides near-optimum solutions to projects with hundreds of activities. The IBM ILOG modeling software and its CPLEX-CP solver engine have been used to develop the proposed CP optimization model for solving the multi-mode resource-constrained project scheduling problem. The model takes many constraints into account, including project deadline, penalty (liquidated damages), incentive, and multiple resource constraints. The paper compares the CP results with the results of other methods, such as heuristic and genetic algorithm optimization, on case studies from the literature to prove the practicality and usefulness of the CP model. The paper also reports the results of CP optimization on larger projects of 1,000 to 2000 activities, which is common in construction practice, and is too large to be solvable by other methods. This research contributes to developing a practical decision support system for resolving real-life constraints in construction projects.