Landslide risk assessment (LRA) is of great significance to hazard prevention and mitigation. However, the historical landslide information is incomplete in most areas, which makes the landslide quantitative risk assessment (LQRA) extremely difficult. This research proposed a set of frameworks for LQRA, so as to achieve LQRA in areas with incomplete historical landslide information. Firstly, we constructed the convolutional neural network (CNN) model suitable for landslide susceptibility assessment (LSA) by studying the structure and hyperparameters optimization of CNN. Secondly, we proposed a method to calculate the temporal probability by using the Poisson model based on the time range of historical landslides occurrence, and then conducted landslide hazard assessment (LHA). Then, we established a mathematical model for landslide intensity of shallow landslide based on landslide area and slope, aiming at solving the problem that it is difficult to calculate landslide intensity due to the lack of landslide volume and velocity. Based on the landslide intensity and the hazard-resistant capacity of the element at risk, we assessed the landslide vulnerability. Finally, population risk map and economic risk map are obtained based on the landslide hazard, vulnerability, and estimated value of the elements at risk. The proposed LQRA framework was applied to Tumen City, China for testing and field validation. From the results, the CNN model built can help improve the accuracy of LSA. The proposed temporal probability calculation method is conducive to the completion of LHA in areas with incomplete historical landslide information. The established landslide intensity mathematical model has certain credibility. Since the landslide risk map is obtained through appropriate simplification and substitution estimation, its final value cannot be used as an accurate prediction of future losses, but it can be used as a reference for the extent of potential losses, so as to determine the areas where hazard prevention and mitigation measures need to be taken.