Overlapping community structure is a significant feature of large-scale complex networks. Some existing community detection algorithms cannot be applied to large-scale complex networks due to their high time or space complexity. Label propagation algorithms were proposed for detecting communities in large-scale networks because of their linear time complexity, however most of which can only detect non-overlapping communities, or the results are inaccurate and unstable. Aimed at the defects, we proposed an improved overlapping community detection algorithm, LPANNI (Label Propagation Algorithm with Neighbor Node Influence), which detects overlapping community structures by adopting fixed label propagation sequence based on the ascending order of node importance and label update strategy based on neighbor node influence and historical label preferred strategy. Extensive experimental results in both real networks and synthetic networks show that, LPANNI can significantly improve the accuracy and stability of community detection algorithms based on label propagation in large-scale complex networks. Meanwhile, LPANNI can detect overlapping community structures in large-scale complex networks under linear time complexity.