Focusing on the problem that the best neighbor nodes of the communities can not accurately be found in most local community detection algorithms, an improved local community detection algorithm was proposed based on local modularity. The concept of node intimacy was introduced to quantify the relationship between the community and the neighbor nodes by the algorithm, and the nodes were selected into the communities according to the node intimacy in descending order. In the end,the extension of the local community was terminated by the local modularity index. Compared with the four kinds of typical community detection algorithms such as the random walk algorithm based on information compression, the algorithm was applied in the real networks and the artificial simulation network. The comprehensive evaluation indexs (F1score) and Normalized Mutual Informations (NMI) of the results are better than comparison algorithms. The experiments show that the algorithm has better efficiency and accuracy, and is very suitable for community detection in a large scale network.