With the increasing of social network, social recommendation becomes hot research topic in recommendation systems. Matrix factorization based (MF-based) recommendation model gradually becomes the key component of social recommendation due to its high expansibility and flexibility. Thus, this paper focuses on MF-based social recommendation methods. Firstly, it reviews the existing social recommendation models according to the model construction strategies. Next, it conducts a series of experiments on real-world datasets to demonstrate the performance of different social recommendation methods from three perspectives including whole-users, cold start-users, and long-tail items. Finally, the paper analyzes the problems of MF-based social recommendation model, and discusses the possible future research directions and development trends in this research area.