As an important physical chemistry property, solubility is still a popular research topic. Its theoretical calculation method has developed rapidly. In particular, the artificial neural network (ANN) has attracted the attention of researchers because of its unique nonlinear processing ability. This review provides a brief explanation of the ANN approaches that are most commonly applied to predict gas solubility in polymers, and states the implementation principle, progress, and performance analysis of hybrid ANNs based on the intelligence algorithm. The prospect of solubility prediction based on current research trends is then proposed. This review attempts to analyze the solubility calculation method and provides an insight into and reference for the application of the artificial intelligence method in chemistry and material fields, and can expand in the future because of the increasing number of solubility prediction approaches being introduced.