This paper proposes an analysis method to check the schedulability of a set of sporadic tasks under earliest deadline first (EDF) scheduler. The sporadic task model consists of subtasks with precedence constraints, arbitrary arrival times and deadlines. In order to determine the schedulability, we present an approach to find exact worst case response time (WCRT) of subtatsks. With the technique presented in this paper, we exploit the precedence relations between subtasks in an accurate way while taking advantage of the deadline of different subtasks. Another nice feature of our approach is that it avoids calculation time overhead by exploiting the concept of deadline busy period. Experimental results show that this consideration leads to a significant improvement compared with existing work.