Recent neurological studies have shown the importance of dendrites in neural computation. In this paper, a neuron model with dendrite morphology, called the logic dendritic neuron model (LDNM), is proposed for classification. This model consists of four layers: a synaptic layer, a dendritic layer, a membrane layer, and a soma body. After training, the LDNM is simplified by proprietary pruning mechanisms and is further transformed into a logic circuit classifier. Moreover, to address the high-dimensional challenge, feature selection is employed as the dimension reduction method before training the LDNM. In addition, the effort of employing a heuristic optimization algorithm as the learning method is also undertaken to speed up the convergence. Finally, the performance of the proposed model is assessed by five benchmark high-dimensional classification problems. In comparison with the other six classical classifiers, LDNM achieves the best classification performance on two (out of five) classification problems. The experimental results demonstrate the effectiveness of the proposed model. A new perspective for solving classification problems by the proposed LDNM is provided in the paper.