Matrix factorization is one of the most popular techniques for prediction problems in the fields of intelligent systems and data mining. It has shown its effectiveness in many real-world applications such as recommender systems. As a collaborative filtering method, it gives users recommendations based on their previous preferences (or ratings). Due to the extreme sparseness of the ratings matrix, active learning is used for eliciting ratings for a user to get better recommendations. In this paper, we propose a new matrix factorization model called Enhanced SVD (ESVD) which combines the classic matrix factorization method with a specific rating elicitation strategy. We evaluate the proposed ESVD method on the Movielens data set, and the experimental results suggest its effectiveness in terms of both accuracy and efficiency, when compared with traditional matrix factorization methods and active learning methods.