Recently, optical neural networks (ONNs) integrated into photonic chips have received extensive attention because they are expected to implement the same pattern recognition tasks in electronic platforms with high efficiency and low power consumption. However, there are no efficient learning algorithms for the training of ONNs on an on-chip integration system. In this article, we propose a novel learning strategy based on neuroevolution to design and train ONNs. Two typical neuroevolution algorithms are used to determine the hyper-parameters of ONNs and to optimize the weights (phase shifters) in the connections. To demonstrate the effectiveness of the training algorithms, the trained ONNs are applied in classification tasks for an iris plants dataset, a wine recognition dataset and modulation formats recognition. The calculated results demonstrate that the accuracy and stability of the training algorithms based on neuroevolution are competitive with other traditional learning algorithms. In comparison to previous works, we introduce an efficient training method for ONNs and demonstrate their broad application prospects in pattern recognition, reinforcement learning and so on.