The occurrence of partial discharge (PD) serves as an indication of power equipment failure, which, if not given due attention, may result in severe power accidents. Traditionally, the detection of PD involves applying various pre-processing techniques to the original signal and extracting specialized signal features that are subsequently classified using a classifier. The process is intricate and demands extensive expertise. One drawback of the conventional detection approach lies in its failure to consider the information conveyed between the phases of a three-phase electrical signal during the process of identifying PD in medium voltage three-phase cables. The present study proposes a novel method for detecting PDs, which is based on channel-wise convolution and channel mixing(C2CM) using full convolutional networks. Firstly, a set of pulses for each phase of a three-phase signal is extracted and combined to form a three-phase pulse set, serving as the input to the network. Subsequently, we introduce a FCN-C2CM network designed specifically for PD detection, capable of learning both the time-domain features of the input signal and the phase features of the three-phase signal, thereby enhancing recognition accuracy. We evaluated our approach using online testing tools on publicly available datasets, with experimental results demonstrating its superiority over existing.