Predicting links in complex networks has been one of the essential topics within the realm of data mining and science discovery over the past few years. This problem remains an attempt to identify future, deleted, and redundant links using the existing links in a graph. Local random walk is considered to be one of the most well-known algorithms in the category of quasi-local methods. It traverses the network using the traditional random walk with a limited number of steps, randomly selecting one adjacent node in each step among the nodes which have equal importance. Then this method uses the transition probability between node pairs to calculate the similarity between them. However, in most datasets, this method is not able to perform accurately in scoring remarkably similar nodes. In the present article, an efficient method is proposed for improving local random walk by encouraging random walk to move, in every step, towards the node which has a stronger influence. Therefore, the next node is selected according to the influence of the source node. To do so, using mutual information, the concept of the asymmetric mutual influence of nodes is presented. A comparison between the proposed method and other similarity-based methods (local, quasi-local, and global) has been performed, and results have been reported for 11 real-world networks. It had a higher prediction accuracy compared with other link prediction approaches.