The development of explainable machine learning methods is attracting increasing attention. Dendritic neuron models have emerged as powerful machine learning methods in recent years. However, providing explainability to a dendritic neuron model has not been explored. In this study, we propose a logic dendritic neuron model (LDNM) and discuss its characteristics. Then, we use a tree-based model called the morphology of decision trees (MDT) to approximate LDNM to gain its explainability. Specifically, a trained LDNM is simplified by a proprietary structure pruning mechanism. Then, the pruned LDNM is further transformed into an MDT, which is easy to understand, to gain explainability. Finally, six benchmark classification problems are used to verify the effectiveness of the structure pruning and MDT transformation. The experimental results show that MDT can provide competitive classification accuracy compared with LDNM, and the concise structure of MDT can provide insight into how the classification results are concluded by LDNM. This paper provides a global surrogate explanation approach for LDNM.