Decisions made by machine learning models can have lasting impacts, making long-term fairness a critical consideration. It has been observed that ignoring the long-term effect and directly applying fairness criterion in static settings can actually worsen bias over time. To address biases in sequential decision-making, we introduce a long-term fairness concept named Equal Long-term BEnefit RaTe (ELBERT). This concept is seamlessly integrated into a Markov Decision Process (MDP) to consider the future effects of actions on long-term fairness, thus providing a unified framework for fair sequential decision-making problems. ELBERT effectively addresses the temporal discrimination issues found in previous long-term fairness notions. Additionally, we demonstrate that the policy gradient of Long-term Benefit Rate can be analytically simplified to standard policy gradients. This simplification makes conventional policy optimization methods viable for reducing bias, leading to our bias mitigation approach ELBERT. Extensive experiments across various diverse sequential decision-making environments consistently reveal that ELBERT-PO significantly diminishes bias while maintaining high utility.