The formation mechanism of landslide disasters is complicated and there are many influencing factors. It is imperative to explore a low-cost and highly applicable method to manage and prevent landslide disasters. As a hot spot in the current artificial intelligence field, deep learning can better simulate the formation of landslide disasters and accurately predict potential slopes. Thus, to explore the application potential of deep learning, this paper constructs one-dimensional, two-dimensional, and three-dimensional forms of landslide data, and then introduces three Convolutional Neural Networks (CNN)-based landslide susceptibility analysis frameworks, including CNN-based classifiers, integrated models, and ensemble models. The proposed deep learning methods were applied to Yanshan County, Jiangxi Province for experiments. 16 landslide influencing factors were first selected for modelling based on the geomorphological, hydrological, and geological environment conditions of the study area. These factors include altitude, aspect, distance to faults, land use, lithology, normalized difference vegetation index, plan curvature, profile curvature, rainfall, distance to rivers, distance to roads, slope, soil, stream power index, sediment transport index, and topographic wetness index. Then, the multi-collinearity analysis and relief-F algorithm were used to analyze and screen the influencing factors. All CNN-based methods were constructed and validated based on several statistical measures of accuracy, root mean square error, mean absolute error, sensitivity, specificity, and the receiver operation characteristic curve. Finally, the susceptibility value of each pixel in the study area was predicted based on the CNN-based methods, and the entire study areas were reclassified into five susceptibility categories: very low, low, moderate, high, and very high. The factor analysis results show that the plan curvature, profile curvature, stream power index, and sediment transport index are redundant factors and should be removed from further modelling process. The model evaluation results demonstrate that all CNN-based models can obtain accurate and reliable landslide susceptibility mapping results. The two-dimensional CNN model achieved the highest prediction accuracy of 78.95% among single CNN models. Moreover, the performance of logistic regression was effectively improved by combining the two-dimensional CNN for feature extraction, with an accuracy improvement of 7.9%. Besides, the heterogeneous ensemble strategy can greatly improve landslide prediction accuracy when using CNN classifiers, with an accuracy improvement between 4.35% and 8.78%. Generally, the CNN has been proven to have huge application potential in landslide susceptibility analysis and can be implemented in other landslide-prone areas with similar geo-environmental conditions.