This research studies resource constrained project scheduling problem in a part of a refinery construction project in real world. In real world, most of the activities are new and we have problems such as activity duration uncertainty. This problem causes a change in a project makespan. The RCPSP is NP-hard. Hence, we proposed an optimization method based on simulated annealing to solve the RCPS Problem. In this paper, Fuzzy sets theory is used to represent this activity duration uncertainty. Used schedule generation scheme, in the proposed simulated annealing algorithm, is a fuzzy parallel scheduling generation method. Proposed algorithm generates the minimum project makespan while considers renewable resource-constrained and activity precedence and also has ability to perform with fuzzy numbers for presenting project details such as start and final time of activities and project whole time with fuzzy numbers. Finally, the results of the algorithm will be evaluated and it will be represented that the proposed algorithm is very efficient and can be used by managers and scheduling programmers in real projects.