Wildfire susceptibility is of great importance to the prevention and management of global wildfires. Artificial neural networks (ANNs), particularly multilayer perceptrons (MLPs), have been widely used in wildfire susceptibility. Recently, deep neural networks (DNNs) have become state-of-the-art algorithms, especially convolutional neural networks (CNNs). However, the applicability of different ANNs in wildfire susceptibility has not been thoroughly discussed, and the interpretability of CNNs remains problematic. This paper consists of two parts: one part deeply compares and analyses the application of two feedforward neural network models (a CNNs and an MLPs) in global wildfire susceptibility prediction, and the other part explores the interpretability of the CNNs model. By constructing response variables from the Global Fire Atlas (GFA) and monthly wildfire predictors, four MLPs and CNNs architectures (namely, the pixel-based CNN-1D and MLP-1D models and the grid-based CNN-2D and MLP-2D models) are constructed for four seasons from 2003 to 2016. After model training, validation and testing, seasonal global susceptibility maps are constructed, and the seasonal peaks in fire activity and highly fire-prone areas can be adequately reflected. Finally, five statistical measures (i.e., the overall accuracy, recall, precision, F1 score, and kappa coefficient), the receiver operating characteristic (ROC) curve, area under the ROC curve (AUC), and Wilcoxon signed-rank tests (WSRTs), were used to evaluate the prediction performance of the models. The results show that the contextual-based CNN-2D model can make full use of the neighbourhood information and has the highest accuracy, the MLPs model is more suitable for pixel-based classification, and the performance ranking of the four models is CNN-2D > MLP-1D > MLP-2D > CNN-1D. In addition, the interpretability of the CNNs was explored using an improved permutation importance (PI) algorithm and partial dependence plots (PDPs). The PI algorithm shows that explanatory variables such as maximum temperature (Tasmax), soil temperature (SoilTemp), normalized difference vegetation index (NDVI) and accumulated precipitation (AccuPre) have a large impact on the model in the four seasons, and the nine one-way and two two-way PDPs perfectly represent how the predictor variables influence the prediction on average.