Graph Convolutional Network (GCN) is adopted to tackle the problem of convolution operation in non-Euclidean space. Previous works on GCN have made some progress, however, one of their limitations is that the design of Adjacency Matrix (AM) as GCN input requires domain knowledge and such process is cumbersome, tedious and error-prone. In addition, entries of a fixed Adjacency Matrix are generally designed as binary values (i.e., ones and zeros) which can not reflect the real relationship between nodes. Meanwhile, many applications require a weighted and dynamic Adjacency Matrix instead of an unweighted and fixed AM, and there are few works focusing on designing a more flexible Adjacency Matrix. To that end, we propose an end-to-end algorithm to improve the GCN performance by focusing on the Adjacency Matrix. We first provide a calculation method called node information entropy to update the matrix. Then, we perform the search strategy in a continuous space and introduce the Deep Deterministic Policy Gradient (DDPG) method to overcome the drawback of the discrete space search. Finally, we integrate the GCN and reinforcement learning into an end-to-end framework. Our method can automatically define the Adjacency Matrix without prior knowledge. At the same time, the proposed approach can deal with any size of the matrix and provide a better AM for network. Four popular datasets are selected to evaluate the capability of our algorithm. The method in this paper achieves the state-of-the-art performance on Cora and Pubmed datasets, with the accuracy of 84.6% and 81.6% respectively.