Due to the complex reservoir conditions and multi-scale pore structure of shale gas, the production shows significant nonlinear characteristics over time. Traditional production prediction methods, which rely on statistical analysis of geological and engineering data, find it difficult to adapt to the complexity of geological conditions and thus cannot achieve high accuracy. A method that combines the hyperbolic decline model with a composite function having time attributes was proposed. The improved A-PSO (adaptive particle swarm optimization algorithm) was used to find the optimal model parameters, establishing a composite time hyperbolic decline model. The research results show as follows. The A-PSO optimization algorithm can automatically adjust parameters and model structure according to the complexity of production data and data changes, finding the optimal parameter combination more quickly and accurately, thereby improving prediction accuracy. The production fluctuates greatly over time, making it difficult for conventional decline models to reflect its characteristics. The composite time decline model, with its strong flexibility, can consider the complexity and variability of oil and gas reservoirs, more accurately describe the production changes of shale gas wells at different stages, and provide higher fitting accuracy, making the production prediction closer to the actual value.