Matrix Factorization (MF) is a very popular method for recommendation systems. It assumes that the underneath rating matrix is low-rank. However, this assumption can be too restrictive to capture complex relationships and interactions among users and items. Recently, Local LOw-Rank Matrix Approximation (LLORMA) has been shown to be very successful in addressing this issue. It just assumes the rating matrix is composed of a number of low-rank submatrices constructed from subsets of similar users and items. Although LLORMA outperforms MF, how to construct such submatrices remains a big problem. Motivated by the availability of rich social connections in today's recommendation systems, we propose a novel framework, i.e., Social LOcal low-rank Matrix Approximation (SLOMA), to address this problem. To the best of our knowledge, SLOMA is the first work to incorporate social connections into the local low-rank framework. Furthermore, we enhance SLOMA by applying social regularization to submatrices factorization, denoted as SLOMA++. Therefore, the proposed model can benefit from both social recommendation and the local low-rank assumption. Experimental results from two real-world datasets, Yelp and Douban, demonstrate the superiority of the proposed models over LLORMA and MF.