Real-time scheduling and analysis of parallel tasks modeled as directed acyclic graphs (DAG) have been intensively studied in recent years. The degree of parallelism of DAG tasks is an important characterization in scheduling. This paper revisits the definition and the computing algorithms for the degree of parallelism of DAG tasks, and clarifies some misunderstandings regarding the degree of parallelism which exist in real-time literature. Based on the degree of the parallelism, we propose a real-time scheduling approach for DAG tasks, which is quite simple but rather effective and outperforms the state-of-the-art by a considerable margin.