Motivated by the concepts of quantum mechanics and particle swarm optimization (PSO), quantum-behaved particle swarm optimization (QPSO) was developed to achieve better global search ability. This paper proposes a new method to improve the global search ability of QPSO with fractional calculus (FC). Based on one of the most frequently used fractional differential definitions, the Grünwald-Letnikov definition, we introduce its discrete expression into the position updating of QPSO. Extensive experiments on well-known benchmark functions were performed to evaluate the performance of the proposed fractional-order quantum particle swarm optimization (FQPSO). The experimental results demonstrate its superior ability in achieving optimal solutions for several different optimizations.