There is great attention to develop hardware accelerator with better energy efficiency, as well as throughput, than GPUs for convolutional neural network (CNN). The existing solutions have relatively limited parallelism as well as large power consumption (including leakage power). In this paper, we present a resistive random access memory (ReRAM)-accelerated CNN that can achieve significantly higher throughput and energy efficiency when the CNN is trained with binary constraints on both weights and activations, and is further mapped on a digital ReRAM-crossbar. We propose an optimized accelerator architecture tailored for bitwise convolution that features massive parallelism with high energy efficiency. Numerical experiment results show that the binary CNN accelerator on a digital ReRAM-crossbar achieves a peak throughput of 792 GOPS at the power consumption of 4.5 mW, which is 1.61 times faster and 296 times more energy-efficient than a high-end GPU.