Neural process (NP) combines the advantages of neural networks and Gaussian processes to estimate uncertainty distribution functions from a small number of contexts and implement function regression. It has been applied to a variety of machine learning tasks such as data complementation and classification. However, for 2D data regression problems (e.g., image data completion), the prediction accuracy of NP and the fitting of the contexts are deficient. To this end, an image-faced neural process (IFNP) is constructed by integrating a convolutional neural network (CNN) into the neural process based on the lower bound of evidence and loss function derivation. Then, a local pooled attention (LPA) module and a global cross-attention (GCA) module are designed for the IFNP, and an image-faced attentive neural process (IFANP) model with significantly better performance than the NP and IFNP is constructed. Finally, these models are applied to MNIST and CelebA datasets, and the scalability of IFNP is demonstrated by combining qualitative and quantitative analysis. In addition, the better data completion and detail-fitting ability of IFNP are confirmed.