Solving large-scale sparse linear systems of equations (SLSEs) is one of the most common and fundamental problems in big data, but it is very challenging for resource-limited users. Cloud computing has been proposed as a timely, efficient, and cost-effective way of solving such expensive computing tasks. Nevertheless, one critical concern in cloud computing is data privacy. Specifically, clients' SLSEs usually contain private information that should remain hidden from the cloud for ethical, legal, or security reasons. Many previous works on secure outsourcing of linear systems of equations (LSEs) have high computational complexity, and do not exploit the sparsity in the LSEs. More importantly, they share a common serious problem, i.e., a huge number of memory I/O operations. This problem has been largely neglected in the past, but in fact is of particular importance and may eventually render those outsourcing schemes impractical. In this paper, we develop an efficient and practical secure outsourcing algorithm for solving large-scale SLSEs, which has low computational and memory I/O complexities and can protect clients' privacy well. We implement our algorithm on Amazon Elastic Compute Cloud, and find that the proposed algorithm offers significant time savings for the client (up to 74 percent) compared to previous algorithms.