This paper presents a multi-start variable neighborhood simulated annealing (MVNSA) algorithm for solving resource-constrained project scheduling problems (RCPSP) to minimize project makespan and maximize schedule robustness. The MVNSA applies a multi-pass process to continually improve a heuristic initial solution. Each pass consists of multiple periods during which the MVNSA iteratively destructs the current solution and reconstructs it according to a heuristic rule until a stopping criterion is met. The MVNSA solves the RCPSP by adding disjunctive arcs into project networks to resolve resource conflicts, so that the resulting networks are precedence and resource feasible. A full factorial computational experiment is set up citing instances from problem library PSPLIB. Computational results show that the MVNSA can generate project schedules with short project makespan and high schedule robustness.