This paper presents a new mixed integer model for a special project resource scheduling problem. Project resource scheduling problems are involved in many complicating factors in real world, such as budget limitation and activity compressibility while considering a finite number of renewable resources. Activity compressibility is modeled through a time / cost trade-off relation between the time and cost of performing each activity. In other words, each activity could be performed in a time interval bounded by activity normal time and activity crash time by paying its corresponding costs. As the problem is known to be NP-Hard, a new heuristic solution method is developed to obtain a near optimal resource schedule in a deterministic project planning problem. The algorithm is run on a set of test data and computational experiences report about the superior performance of the algorithm than the existing methods.