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The spatial variability of the properties of natural soils is one of the major sources of uncertainties that can influence the performance of geotechnical structures. The direct Monte-Carlo simulation (MCS) method, although robust and versatile, may incur prohibitively high computational burdens, especially for cases involving low failure probability levels. In this paper, a hybrid strategy that fuses convolutional neural networks (CNNs) and maximum entropy distribution with fractional moments (MaxEnt-FM) is proposed. MaxEnt-FM is a post-processing technique that fits a probability distribution to a set of sample data. The proposed hybrid strategy starts by training a CNN as the metamodel of the time-demanding random field finite element model. The trained CNN is then used to generate sample data, which is subsequently processed using the MaxEnt-FM technique to obtain failure probability. The use of a CNN allows MaxEnt-FM to be carried out without explicit calls to the finite element model. Therefore, the proposed hybrid strategy has the potential to provide a computationally efficient technique to calculate failure probability. For the illustrative slope stability example that has a failure probability of 3 × 10−4, the proposed hybrid strategy yields a less than 10% error in the predicted failure probability with only hundreds of finite element simulations.