Image demoireing is a multi-faceted image restoration task involving both texture and color restoration. In this paper, we propose a novel multiscale bandpass convolutional neural network (MBCNN) to address this problem. As an end-to-end solution, MBCNN respectively solves the two sub-problems. For texture restoration, we propose a learnable bandpass filter (LBF) to learn the frequency prior for moire texture removal. For color restoration, we propose a two-step tone mapping strategy, which first applies a global tone mapping to correct for a global color shift, and then performs local fine tuning of the color per pixel. Through an ablation study, we demonstrate the effectiveness of the different components of MBCNN. Experimental results on two public datasets show that our method outperforms state-of-the-art methods by a large margin (more than 2dB in terms of PSNR).