Compressive sensing is a new signal acquisition paradigm that enables sparse/compressible signal to be sampled under the Nyquist-rate. To fully benefit from its much simplified acquisition process, huge efforts have been made on improving the performance of compressive sensing recovery. However, concerning color images, compressive sensing recovery lacks in addressing image characteristics like energy distribution or human visual system. In order to overcome the problem, this paper proposes a new group-sparsity hard thresholding process by preserving some RGB-grouped coefficients important in both terms of energy and perceptual sensitivity. Moreover, a smoothed group-sparsity iterative hard thresholding algorithm for compressive sensing of color images is proposed by incorporating a frame-based filter with group-sparsity hard thresholding process. In this way, our proposed method not only pursues sparsity of image in transform domain but also pursues smoothness of image in spatial domain. Experimental results show average PSNR gains up to 2.7dB over the state-of-the-art group-sparsity smoothed recovery method.