The cooperative navigation algorithm is the crucial technology for multirobot systems to accomplish autonomous collaborative operations, and it is still a challenge for researchers. In this work, we propose a new multiagent reinforcement learning algorithm called multiagent local-and-global attention actor-critic (MLGA2C) for multiagent cooperative navigation. Inspired by the attention mechanism, we design the local-and-global attention module to dynamically extract and encode critical environmental features. Meanwhile, based on the centralized training and decentralized execution (CTDE) paradigm, we extend a new actor-critic method to handle feature encoding and make navigation decisions. We also evaluate the proposed algorithm in two cooperative navigation scenarios: static target navigation and dynamic pedestrian target tracking. The multiple experimental results show that our algorithm performs well in cooperative navigation tasks with increasing agents.