For Resource-Constrained Multi-Project Scheduling Problem (RCMPSP), a simulated harmonic oscillator algorithm was introduced. By simulating the change of potential energy state in harmonic vibration system, the classical harmonic vibration stage was transformed to quantum harmonic vibration stage, and the algorithm achieved the change process from the global search to local search. Meanwhile, the two-stage search guarantees convergence accuracy and search efficiency of the algorithm. Combined with method based on order and serial schedule generation scheme and multi-project task list, the gotten scheduling scheme can meet the project schedule constraints of precedence relations. The tests on standard test functions indicate that the algorithm has high search efficiency and accuracy. Finally, three groups of multi-project scheduling examples were given.