A person tends to generate dynamic attention towards speech under complicated environments. Based on this phenomenon, we propose a framework combining dynamic attention and recursive learning together for monaural speech enhancement. Apart from a major noise reduction network, we design a separated sub-network, which adaptively generates the attention distribution to control the information flow throughout the major network. To effectively decrease the number of trainable parameters, recursive learning is introduced, which means that the network is reused for multiple stages, where the intermediate output in each stage is correlated with a memory mechanism. As a result, a more flexible and better estimation can be obtained. We conduct experiments on TIMIT corpus. Experimental results show that the proposed architecture obtains consistently better performance than recent state-of-the-art models in terms of both PESQ and STOI scores.