The increasing number of space debris has created an orbital debris environment that poses increasing impact risks to existing space systems and human space flights. For the safety of in-orbit spacecrafts, we should optimally schedule surveillance tasks for the existing facilities to allocate resources in a manner that most significantly improves the ability to predict and detect events involving affected spacecrafts. This paper analyzes two criteria that mainly affect the performance of a scheduling scheme and introduces an artificial intelligence algorithm into the scheduling of tasks of the space debris surveillance network. A new scheduling algorithm based on the particle swarm optimization algorithm is proposed, which can be implemented in two different ways: individual optimization and joint optimization. Numerical experiments with multiple facilities and objects are conducted based on the proposed algorithm, and simulation results have demonstrated the effectiveness of the proposed algorithm.