Deep neural networks (DNNs) have been applied to recover signals in optical communication systems and have shown competence of mitigating linear and nonlinear distortions. However, as the data throughput increases, the heavy computational cost of DNNs impedes them from rapid and power-efficient processing. In this paper, we propose an optical communication signal recovery technology based on a photonic convolutional processor, which is realized by dispersion delay unit and wavelength division multiplexing. Based on the photonic convolutional processor, we implement an optoelectronic convolutional neural network (OECNN) for signal post-equalization and experimentally demonstrate on 16QAM and 32QAM of an optical wireless communication system. With system parameters optimization, we verify that the OECNN can achieve accurate signal recovery where the bit error ratio (BER) is below the 7% forward error correction threshold of 3.8×10-3 at 2Gbps. With adding the OECNN-based nonlinear compensation, compared with only linear compensation, we improve the quality (Q) factor by 3.35 dB at 16QAM and 3.30 dB at 32QAM, which is comparable to that of an electronic neural network. This work proves that the photonic implementation of DNN is promising to provide a fast and power-efficient solution for optical communication signal processing.