Abstract-Expert finding for question answering is a challenging problem in community-based question answering (CQA) systems, arising in many real applications such as question routing and identification of best answers. In order to provide high-quality experts, many existing approaches learn the user model from their past question-answering activities in CQA systems. However, the past activities of users in most CQA systems are rather few, and thus the user model may not be well inferred in practice. In this paper, we consider the problem of expert finding from the viewpoint of missing value estimation. We then employ users' social networks for inferring user model, and thus improve the performance of expert finding in CQA systems. In addition, we develop a novel graph-regularized matrix completion algorithm for inferring the user model. We further develop two efficient iterative procedures, GRMC-EGM and GRMC-AGM, to solve the optimization problem. GRMC-EGM utilizes the Extended Gradient Method (EGM), while GRMC-AGM applies the Accelerated proximal Gradient search Method (AGM), for the optimization. We evaluate our methods on the well-known question answering system Quora, and the popular social network Twitter. Our empirical study shows the effectiveness of the proposed algorithms in comparison to the state-of-the-art expert finding algorithms.