In this paper, an improved community detection algorithm based on the modularity is proposed. The existing algorithm does not consider the information that the nodes have in checking the possible modularity increase, hence the computation may be inefficient. The proposed algorithm computes the node degree (weight) and sorts them in non-increasing order. By checking the possible modularity value increase for the nodes in the nonincreasing order of node weights, the algorithm finds the final solution more quickly than the existing algorithm does. Through the computational experiments, it is shown that the proposed algorithm finds a modularity as good as the existing algorithm obtains.