Deep learning that utilizes large-scale deep neural networks (DNNs) is effective in automatic high-level feature extraction but also computation and memory intensive. Constructing DNNs using blockcirculant matrices can simultaneously achieve hardware acceleration and model compression while maintaining high accuracy. This paper proposes HSIM-DNN, an accurate hardware simulator on the C++ platform, to simulate the exact behavior of DNN hardware implementations and thereby facilitate the block-circulant matrix-based design of DNN training and inference procedures in hardware. Real FPGA implementations validate the simulator with various circulant block sizes and data bit lengths taking into account accuracy, compression ratio and power consumption, which provides excellent insights for hardware design.