Optimized convolutional neural network (CNN) models and energy-efficient hardware design are of great importance in edge-computing applications. The neural architecture search (NAS) methods are employed for CNN model optimization with multi-precision networks. To satisfy the computation requirements, multi-precision convolution accelerators are highly desired. The existing high-precision-split (HPS) designs reduce the additional logics for reconfiguration while resulting in low throughput for low precisions. The low-precision-combination (LPC) designs improve the low-precision throughput with large hardware cost. In this work, a bit-split-and-combination (BSC) systolic accelerator is proposed to overcome the bottlenecks. Firstly, BSC-based multiply-accumulate (MAC) unit is designed to support multi-precision computation operations. Secondly, multi-precision systolic dataflow is developed with improved data-reuse and transmission efficiency. The proposed work is designed by Chisel and synthesized in 28-nm process. The BSC MAC unit achieves maximum 2.40× and 1.64× energy efficiency than HPS and LPC units, respectively. Compared with published accelerator designs Gemmini, Bit-fusion and Bit-serial, the proposed accelerator achieves up to 2.94 × area efficiency and 6.38 × energy-saving performance on the multi-precision VGG-16, ResNet-18 and LeNet-5 benchmarks.