Multi-agent path finding in dynamic crowded environments is of great academic and practical value for multi-robot systems in the real world. To improve the effectiveness and efficiency of communication and learning process during path planning in dynamic crowded environments, we introduce an algorithm called Attention and BicNet based Multi-agent path planning with effective reinforcement (AB-Mapper)under the actor-critic reinforcement learning framework. In this framework, on the one hand, we utilize the BicNet with communication function in the actor-network to achieve intra team coordination. On the other hand, we propose a centralized critic network that can selectively allocate attention weights to surrounding agents. This attention mechanism allows an individual agent to automatically learn a better evaluation of actions by also considering the behaviours of its surrounding agents. Compared with the state-of-the-art method Mapper,our AB-Mapper is more effective (85.86% vs. 81.56% in terms of success rate) in solving the general path finding problems with dynamic obstacles. In addition, in crowded scenarios, our method outperforms the Mapper method by a large margin,reaching a stunning gap of more than 40% for each experiment.