In this paper, we introduce a novel utility accrual scheduling algorithm for real-time cloud computing services. The real-time tasks are scheduled non-preemptively with the objective to maximize the total utility. The most unique characteristic of our approach is that, different from the traditional utility accrual approach that works under one single time utility function (TUF), we have two different TUFs--a profit TUF and a penalty TUF--associated with each task at the same time, to model the real-time applications for cloud computing that need not only to reward the early completions but also to penalize the abortions or deadline misses of real-time tasks. Our experimental results show that our proposed algorithm can significantly outperform the traditional scheduling algorithms such as the Earliest Deadline First (EDF), the traditional utility accrual scheduling algorithm and an early scheduling approach based on the similar model.