Safe and efficient co-planning of multiple robots in pedestrian participation environments is promising for applications. In this work, a novel multi-robot social-aware efficient cooperative planner that on the basis of off-policy multi-agent reinforcement learning (MARL) under partial dimension-varying observation and imperfect perception conditions is proposed. We adopt temporal-spatial graph (TSG)-based social encoder to better extract the importance of social relation between each robot and the pedestrians in its field of view (FOV). Also, we introduce K-step lookahead reward setting in multi-robot RL framework to avoid aggressive, intrusive, short-sighted, and unnatural motion decisions generated by robots. Moreover, we improve the traditional centralized critic network with multi-head global attention module to better aggregates local observation information among different robots to guide the process of individual policy update. Finally, multi-group experimental results verify the effectiveness of the proposed cooperative motion planner.