Bit-serial neural network accelerators address the growing need for compact and energy-efficient deep learning tools. Traditional neural network accelerators, while effective, often grapple with issues of size, power consumption, and versatility in handling a variety of computational tasks. To counter these challenges, this paper introduces an approach that hinges on the integration of bit-serial processing with advanced dataflow techniques and architectural optimizations. Central to this approach is a column-buffering (CB) dataflow, which significantly reduces access and movement requirements for the input feature map (IFM), thereby enhancing efficiency. Moreover, a simplified quantization process effectively eliminates biases, streamlining the overall computation process. Furthermore, this paper presents a meticulously designed LeNet-5 accelerator leveraging a convolutional layer processing element array (CL PEA) architecture incorporating an improved bit-serial multiply–accumulate unit (MAC). Empirically, our work demonstrates superior performance in terms of frequency, chip area, and power consumption compared to current state-of-the-art ASIC designs. Specifically, our design utilizes fewer hardware resources to implement a complete accelerator, achieving a high performance of 7.87 GOPS on a Xilinx Kintex-7 FPGA with a brief processing time of 284.13 μs. The results affirm that our design is exceptionally suited for applications requiring compact, low-power, and real-time solutions.