In this paper, we consider power-aware task scheduling (PATS) in HPC clouds. Users request virtual machines (VMs) to execute their tasks. Each task is executed on one single VM, and requires a fixed number of cores (i.e., processors), computing power (million instructions per second - MIPS) of each core, a fixed start time and non-preemption in a duration. Each physical machine has maximum capacity resources on processors (cores); each core has limited computing power. The energy consumption of each placement is measured for cost calculating purposes. The power consumption of a physical machine is in a linear relationship with its CPU utilization. We want to minimize the total energy consumption of the placements of tasks. We propose here a genetic algorithm (GA) to solve the PATS problem. The GA is developed with two versions: (1) BKGPUGA, which is an adaptively implemented using NVIDIA’s Compute Unified Device Architecture (CUDA) framework; and (2) SGA, which is a serial GA version on CPU. The experimental results show the BKGPUGA program that executed on a single NVIDIA® TESLATM M2090 GPU (512 cores) card obtains significant speedups in comparing to the SGA program executing on Intel® XeonTM E5-2630 (2.3 GHz) on same input problem size. Both versions share the same GA’s parameters (e.g. number of generations, crossover and mutation probability, etc.) and a relative small (10-11) on difference of two finesses between BKGPUGA and SGA. Moreover, the proposed BKGPUGA program can handle large-scale task scheduling problems with scalable speedup under limitations of GPU device (e.g. GPU’s device memory, number of GPU cores, etc.).