In this study, we propose a method for training convolutional neural networks to make them identify and classify images with higher classification accuracy. By combining the Cartesian and polar coordinate systems when describing the images, the method of recognition and classification for plankton images is discussed. The optimized classification and recognition networks are constructed. They are available for in situ plankton images, exploiting the advantages of both coordinate systems in the network training process. Fusing the two types of vectors and using them as the input for conventional machine learning models for classification, support vector machines (SVMs) are selected as the classifiers to combine these two features of vectors, coming from different image coordinate descriptions. The accuracy of the proposed model was markedly higher than those of the initial classical convolutional neural networks when using the in situ plankton image data, with the increases in classification accuracy and recall rate being 5.3% and 5.1% respectively. In addition, the proposed training method can improve the classification performance considerably when used on the public CIFAR-10 dataset.