Convolutional neural network (CNN) models equipped with depth separable convolution (DSC) promise a lower spatial complexity while retaining high model accuracy. However, little attention has been paid to their hardware architecture. Previous studies on DSC-based CNN accelerators typically use fixed computational models for various models, leading to an imbalance between power, efficiency, and performance. To address this problem, a novel, real-time DSC-based CNN accelerator that can accommodate field-programmable gate arrays (FPGAs) of different capacities and CNNs of different sizes is proposed in this paper. Attractively, a dynamically reconfigurable computing engine and block-convolution-based adaptive dataflow scheduling mode strike a trade-off between hardware resources and the processing speed in industrial processes. The proposed MobileNet accelerator was implemented and evaluated on the Xilinx XC7020 platform. Compared to previous FPGA-based accelerators, the experimental results showed that our approach can provide a frame rate of 29.4 FPS for full HD RGB images, meeting the needs of real industrial real-time applications.