The singular value decomposition (SVD) is a widely used matrix factorization tool which underlies plenty of useful applications, e.g. recommendation system, abnormal detection and data compression. Under the environment of emerging Internet of Things (IoT), there would be an increasing demand for data analysis to better human's lives and create new economic growth points. Moreover, due to the large scope of IoT, most of the data analysis work should be done in the network edge, i.e. handled by fog computing. However, the devices which provide fog computing may not be trustable while the data privacy is often the significant concern of the IoT application users. Thus, when performing SVD for data analysis purpose, the privacy of user data should be preserved. Based on the above reasons, in this paper, we propose a privacy-preserving fog computing framework for SVD computation. The security and performance analysis shows the practicability of the proposed framework. Furthermore, since different applications may utilize the result of SVD operation in different ways, three applications with different objectives are introduced to show how the framework could flexibly achieve the purposes of different applications, which indicates the flexibility of the design.