The need for better energy efficiency in grid computing is significant given the massive amount of energy dissipated by large grids. We approximate the optimal allocation of compute nodes to a job stream, with each job consisting of multiple tasks, and while considering both the computing requirements and a desired balance of shorter makespans and lower energy consumption. The approach is widely applicable to many grid scenarios and does not require the scheduler to have administrative rights to change the workers’ DVFS or hibernation state. A discrete particle swarm optimisation (PSO) determines the worker assignments based on estimations of the tasks’ service times and energy consumption using an online learning process, and taking into account pending task executions from prior jobs. The performance of the proposed system is then evaluated through extensive Monte Carlo simulations using traces of real multi-threaded program executions on representative computer hardware. The results demonstrate the latent energy savings that are possible in grid computing through an energy-aware task scheduling.