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Distributed computing, e.g., cluster and cloud computing, has been applied in almost all areas for data processing, while high resource efficiency and user satisfaction are still the ambition of distributed computing. Task scheduling is indispensable for achieving the goal. As the task scheduling problem is NP-hard, heuristics and meta-heuristics are frequently applied. Every method has its own advantages and limitations. Thus, in this paper, we designed a hybrid heuristic task scheduling problem by exploiting the high global search ability of the Genetic Algorithm (GA) and the fast convergence of Particle Swarm Optimization (PSO). Different from existing hybrid heuristic approaches that simply sequentially perform two or more algorithms, the PGA applies the evolutionary method of a GA and integrates self- and social cognitions into the evolution. We conduct extensive simulated environments for the performance evaluation, where simulation parameters are set referring to some recent related works. Experimental results show that the PGA has 27.9–65.4% and 33.8–69.6% better performance than several recent works, on average, in user satisfaction and resource efficiency, respectively.