Collaborative filtering provides a solution for the personalized recommendation to solve the problem of information overload. But the problems of data sparsity and scalability are the serious factors affecting the recommendation quality. To solve these problems, we propose a collaborative filtering algorithm based on singular value decomposition and fuzzy clustering. We retain the number of the total characteristic value through the theory of energy conservation in the special relativity in physics, so as to determine the dimension of dimension reduction. In addition, by using the fuzzy clustering, we also reduce the search range of the neighbors. Compared with traditional collaborative filtering recommendation algorithm in the different data sets of MovieLens and 2013 Baidu movie recommendation system, the proposed algorithm performs better in the recommendation quality.