In view of the friend recommendation problem in social networks, a friend recommendation algorithm based on the theory of three-degree influence was proposed. The relationships between social network users include not only the mutual friends, but also the other connecting relations with different lengths. By introducing the theory of three-degree influence, the algorithm took all the relationships within three-degree between users into account, while not only considering the number of mutual friends between users as the main basis of the friend recommendation. By assigning corresponding weights to connections with different distances, the strength of friend relationship between users could be calculated, which would be used as the standard for recommendation. The experimental results on Sina microblog and Facebook show that the precision and recall rate of the proposed algorithm are improved by about 5% and 0.8% respectively than that merely based on mutual friends, which indicates the better recommendation performance of the improved recommendation algorithm. It can be helpful for the social platform to improve the recommendation system and enhance the user experience.