The massive amount of data that is being collected by today's society has the potential to advance scientific knowledge and boost innovations. However, people often lack sufficient computing resources to analyze their large-scale data in a cost-effective and timely way. Cloud computing offers access to vast computing resources on an on-demand and pay-per-use basis, which is a practical way for people to analyze their huge data sets. However, since their data contain sensitive information that needs to be kept secret for ethical, security, or legal reasons, many people are reluctant to adopt cloud computing. For the first time in the literature, we propose a secure outsourcing algorithm for large-scale quadratic programs (QPs), which is one of the most fundamental problems in data analysis. Specifically, based on simple linear algebra operations, we design a low-complexity QP transformation that protects the private data in a QP. We show that the transformed QP is computationally indistinguishable under a chosen plaintext attack (CPA), i.e., CPA-secure. We then develop a parallel algorithm to solve the transformed QP at the cloud, and efficiently find the solution to the original QP at the user. We implement the proposed algorithm on the Amazon Elastic Compute Cloud (EC2) and a laptop. We find that our proposed algorithm offers significant time savings for the user and is scalable to the size of the QP.