Generalized additive models (GAMs) have long been a powerful white-box tool for the intelligible analysis of tabular data, revealing the influence of each feature on the model predictions. Despite the success of neural networks (NNs) in various domains, their application as NN-based GAMs in tabular data analysis remains suboptimal compared to tree-based ones, and the opacity of encoders in NN-GAMs also prevents users from understanding how networks learn the functions. In this work, we propose a new deep tabular learning method, termed Prototypical Neural Additive Model (ProtoNAM), which introduces prototypes into neural networks in the framework of GAMs. With the introduced prototype-based feature activation, ProtoNAM can flexibly model the irregular mapping from tabular features to the outputs while maintaining the explainability of the final prediction. We also propose a gradient-boosting inspired hierarchical shape function modeling method, facilitating the discovery of complex feature patterns and bringing transparency into the learning process of each network layer. Our empirical evaluations demonstrate that ProtoNAM outperforms all existing NN-based GAMs, while providing additional insights into the shape function learned for each feature. The source code of ProtoNAM is available at \url{https://github.com/Teddy-XiongGZ/ProtoNAM}.