Network structure learning aims to optimize network architectures and make them more efficient without compromising performance. In this paper, we first study the astrocytes, a new mechanism to regulate connections in the classic M-P neuron. Then, with the astrocytes, we propose an AstroNet that can adaptively optimize neuron connections and therefore achieves structure learning to achieve higher accuracy and efficiency. AstroNet is based on our built Astrocyte-Neuron model, with a temporal regulation mechanism and a global connection mechanism, which is inspired by the bidirectional communication property of astrocytes. With the model, the proposed AstroNet uses a neural network (NN) for performing tasks, and an astrocyte network (AN) to continuously optimize the connections of NN, i.e., assigning weight to the neuron units in the NN adaptively. Experiments on the classification task demonstrate that our AstroNet can efficiently optimize the network structure while achieving state-of-the-art (SOTA) accuracy.