Modern organizations have collected vast amounts of data created by various systems and applications. Scientists and engineers have a strong desire to advance scientific and engineering knowledge from such massive data. QR factorization is one of the most fundamental mathematical tools for data analysis. However, conducting QR factorization of a matrix requires high computational complexity. This incurs a formidable challenge in efficiently analyzing large-scale data sets by normal users or small companies on traditional resource limited computers. To overcome this limitation, industry and academia propose to employ cloud computing that can offer abundant computing resources. This, however, raises privacy concerns because users' data may contain sensitive information that needs to be hidden for ethical, legal, or security reasons. To this end, we propose a privacy-preserving outsourcing algorithm for efficiently performing large-scale QR factorization. We implement the proposed algorithm on the Amazon Elastic Compute Cloud (EC2) platform and a laptop. The experiment results show significant time saving for the user.