Scheduling problems have been thoroughly explored by the research community, but they acquire challenging characteristics in grid computing systems. In this context, it is important to have a scheduling strategy that can make efficient use of the available grid resources. This article focuses on the application of the particle swarm optimisation (PSO) meta-heuristic to the scheduling of independent users' jobs on grids. It is shown that the PSO method can achieve satisfactory results in simple problem instances, yet it has a tendency to stagnate around local minima in high-dimensional problems. Therefore, this research also proposes a novel hybrid particle swarm optimisation-genetic algorithm (H_PSO) method that aims to increase swarm diversity when a stagnation condition is detected. This new method is evaluated and compared with other heuristics and PSO formulations; the comparison shows that H_PSO can successfully improve the scheduling solution.72113129