Abstract : In this paper, we consider parallel real-time tasks follow- ing a Directed Acyclic Graph (DAG) model. This task model is classical in embedded and industrial system applications. Each real-time task is defined by a set of subtasks under precedence constraints. With each subtask being associated a worst case execution time and a maximal degree of parallelism. We propose a parallelizing algorithm based on the critical path concept, in which we find the best parallelizing structure of the task according to the response time and the required number of processors, considering the worst case execution time of the subtasks.