Sea surface temperature (SST) is an important factor in the marine environment and has significant impacts on climate, ecology, and maritime activities. Most existing SST prediction methods consider the ocean as a uniform field and use a uniform grid to predict SST. However, the marine environment is a complex system, and factors such as solar radiation, differences in land and sea thermal properties, and ocean circulation lead to uneven spatial distributions of SSTs. We propose a non-uniform grid construction method based on an SST spatial gradient to encode SST data, as well as a Non-uniform Grid Graph Convolutional Network (NGGCN) model. The NGGCN consists of two spatiotemporal modules, each of which extracts spatial features from the GCN module, captures temporal correlations through the GRU module, and performs feature restoration and output results through the fully connected module. We selected data from the Yellow Sea and Bohai Sea to validate the effectiveness of the NGGCN in predicting SST at different time scales and prediction steps. The results indicate that our model shows a significant improvement in prediction performance compared to other models.