<p>Principal component analysis for two-dimensional functional data is a crucial issue in functional data analysis. Most existing methods rely on Karhunen-Loève expansion, which assumes linear structure of the data and may become inefficient when data deviates from the linear assumption. To address this issue, we propose a novel neural network model for conducting principal component analysis on two-dimensional functional data with nonlinear structures. Compared with conventional neural network, our model incorporates weight and bias functions to maintain the characteristics of functional data. Our proposed model eliminates the need to compute the high-cost four-dimensional covariance function. Additionally, we explore the universal approximation property of the proposed model and conduct a simulation study to evaluate its performance. The proposed method is also applied to a real-world dataset to further demonstrate its superiority.</p>