This paper proposes a kernel-blending connection approximated by a neural network (KBNN) for image classification. A kernel mapping connection structure, guaranteed by the function approximation theorem, is devised to blend feature extraction and feature classification through neural network learning. First, a feature extractor learns features from the raw images. Next, an automatically constructed kernel mapping connection maps the feature vectors into a feature space. Finally, a linear classifier is used as an output layer of the neural network to provide classification results. Furthermore, a novel loss function involving a cross-entropy loss and a hinge loss is proposed to improve the generalizability of the neural network. Experimental results on three well-known image datasets illustrate that the proposed method has good classification accuracy and generalizability.