The long-term operation attribute of recycling business determines the dynamic characteristics of its decision-making process. This article considers time-preference heterogeneity for a firm's long-term benefits in a closed-loop supply chain (CLSC) system, that is, the situation in which the leader manufacturer has time-consistent preference and the follower retailer has time-inconsistent preference. Also, the impact of heterogeneous time preference is studied on the decision-making of recovery and pricing strategies and the selection of recycling modes in the CLSC system. Firstly, a stochastic hyperbolic discounting model is applied to construct a dynamic programming model for an inter-temporal decision when the retailer has time-inconsistent preference. Next, by combining the stochastic differential game and the reverse induction method, the equilibrium recycling investment, pricing strategy, expected recyclability rate, and utility functions are obtained under different recycling modes. Then, the equilibrium results are compared and analyzed. The results show that, compared to the mature retailer with time-inconsistent preference, the naive retailer taking responsibility for recycling can ensure the higher utility of the entire CLSC system. When the manufacturer with time-consistent preference is responsible for recycling, whether facing mature or naive retailers, his recycling behavior can promote the effective utilization of waste products, enabling the entire CLSC system to achieve the optimal utility. Therefore, manufacturer recycling mode is best for the CLSC system, and the inconsistency of retailer's time preference increases the willingness of supply chain members to adopt manufacturer recycling strategies, which is different from the research results of completely rational static models.