Breast cancer is a serious disease across the world, and it is one of the largest causes of cancer death for women. The traditional diagnosis is not only time consuming but also easily affected. Hence, artificial intelligence (AI), especially neural networks, has been widely used to assist to detect cancer. However, in recent years, the computational ability of a neuron has attracted more and more attention. The main computational capacity of a neuron is located in the dendrites. In this paper, a novel neuron model with dendritic nonlinearity (NMDN) is proposed to classify breast cancer in the Wisconsin Breast Cancer Database (WBCD). In NMDN, the dendrites possess nonlinearity when realizing the excitatory synapses, inhibitory synapses, constant-1 synapses and constant-0 synapses instead of being simply weighted. Furthermore, the nonlinear interaction among the synapses on a dendrite is defined as a product of the synaptic inputs. The soma adds all of the products of the branches to produce an output. A back-propagation-based learning algorithm is introduced to train the NMDN. The performance of the NMDN is compared with classic back propagation neural networks (BPNNs). Simulation results indicate that NMDN possesses superior capability in terms of the accuracy, convergence rate, stability and area under the ROC curve (AUC). Moreover, regarding ROC, for continuum values, the existing 0-connections branches after evolving can be eliminated from the dendrite morphology to release computational load, but with no influence on the performance of classification. The results disclose that the computational ability of the neuron has been undervalued, and the proposed NMDN can be an interesting choice for medical researchers in further research.