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The tremendous success of convolutional neural network (CNN) has made it ubiquitous in many fields of human endeavor. Many applications such as biomedical analysis and scientific data analysis involve analyzing volumetric data. This spawns huge demand for 3D-CNN. Although accelerators such as GPU may provide higher throughput on deep learning applications, they may not be available in all scenarios. CPU, especially many-core CPU with non-uniform memory access (NUMA) architecture, remains an attractive choice for deep learning inference in many scenarios. In this paper, we propose a distributed inference solution for 3D-CNN that targets on the emerging ARM many-core CPU platform. A hierarchical partition approach is claimed to accelerate 3D-CNN inference by exploiting characteristics of memory and cache on ARM many-core CPU. Based on the hierarchical model partition approach, other optimization techniques such as NUMA-aware thread scheduling and optimization of 3D-img2row convolution are designed to exploit the potential of ARM many-core CPU for 3D-CNN. We evaluate our proposed inference solution with several classic 3D-CNNs: C3D, 3D-resnet34, 3D-resnet50, 3D-vgg11 and P3D. Our experimental results show that our solution can boost the performance of the 3D-CNN inference, and achieve much better scalability, with a negligible fluctuation in accuracy. When employing our 3D-CNN inference solution on ACL libraries, it can outperform naive ACL implementations by 11x to 50x on ARM many-core processor. When employing our 3D-CNN inference solution on NCNN libraries, it can outperform the naive NCNN implementations by 5.2x to 14.2x on ARM many-core processor.