Today's massive amount of biological sequence data has the potential to rapidly advance our understanding of life's processes. However, since analyzing biological sequences is a very expensive computing task, users face a formidable challenge in trying to analyze these data on their own. Cloud computing offers access to a large amount of computing resources in an on-demand and pay-per-use fashion, which is a practical way for people to analyze these huge data sets. However, many people are still reluctant to outsource biological sequences to the cloud because they contain sensitive information that should be kept secret for ethical, security, and legal reasons. One of the most fundamental and frequently used computational tools for biological sequence analysis is pairwise sequence alignment (PSA). Previous works for securely solving PSAs at the cloud suffer from poor scalability, i.e., they are unable to exploit the cloud's infrastructure to solve PSAs in parallel because resource-limited users need to be constantly involved in the computations. In this paper, we develop a secure outsourcing algorithm that allows users to solve an arbitrary number of PSAs in parallel at the cloud. Compared with previous works, our algorithm can reduce computing time of a large number of PSAs by more than 50% with as few as 5 computing nodes at the cloud.