Quadruped　robot　gait　control　is　a　widely　studied　topic,　with　the　advancements　in　artificial　intelligence,　reinforcement　learning-based　approaches　provide　a　promising　solution　for　bionic　gait　learning　of　quadruped　robots.　In　this　study,　we　propose　an　Intelligent　Memory　Soft　Actor-Critic　(IM-SAC)　algorithm　that　uses　the　Soft　Actor-Critic　algorithm　as　the　basic　framework　and　incorporates　Long　Short-Term　Memory　network　(LSTM)　and　Gated　Recurrent　Unit　(GRU)　to　extract　time-sequence-related　sequence　information　of　the　quadruped　robot　motion.　The　IM-SAC　algorithm　aims　to　maximize　the　motion　reward　by　controlling　the　degree　of　memory　and　forgetting　of　sample　information,　giving　priority　to　learning　samples　with　high　reward　values,　and　achieving　faster　cumulative　rewards　and　optimization　models.　We　design　a　reward　function　using　the　quadruped　robot＇s　own　speed,　swing　angle,　and　other　information　to　train　the　robot,　and　use　the　12　motor　angles　as　output　values　to　control　the　movement　of　the　quadruped　robot.　We　conducted　experiments　on　the　Pybullet　platform　to　test　the　algorithm＇s　performance　in　gait　learning　tasks　of　the　quadruped　robot.　The　results　show　that　our　study　provides　a　promising　solution　for　gait　control　of　quadruped　robots　by　integrating　reinforcement　learning　and　intelligent　memory　mechanisms.　©　2023　IEEE.