Nowadays, recommender systems have become a necessity in various applications, especially in a large-scale online shop. In addition to the rating information provided by the users, social relationships of a user begin to be incorporated to further improve the performance of current recommender systems. Among several alternatives, matrix factorization is recognized as an effective technique to reduce data dimensionality and to capture significant latent relationships between users and items. Furthermore, recommender systems are used in an ever-changing commercial environment and usually operate on the large-scale data. Note that there are always new users, items and ratings as time advances, resulting in a rating matrix of increasing size. This poses a challenging problem because decomposing the entire matrix is costly. In this work, we thus propose an incremental scheme to directly update the rating matrix without the need to decompose the entire rating matrix. This helps to achieve better efficiency at the cost of some approximation errors. Experimental results show that our scheme has high efficiency as expected and significantly enhances the recommendation quality for cold-start users.