National audienceEffective scheduling is crucial for task-based applications to achieve high performance in heterogeneous computing systems. These applications are usually represented by directed acyclic graphs (DAG). In this paper, we present a dynamic scheduling technique for DAGs intending to minimize the overall completion time of the parallelized applications. We introduce MulTreePrio, a novel scheduler based on a set of balanced trees data structure. The assignment of tasks to available resources is done according to priority scores per task for each type of processing unit. These scores are computed through heuristics built according to a set of rules that our scheduler should fulfil. We simulate the scheduling on three DAGs coming from numerical kernels with different configurations and we compare its behavior with both dynamic schedulers and static scheduling techniques based on the critical path. We show the efficiency of our scheduler with an average speedup of x2 with respect to the dynamic scheduler and x0,99 compared to the critical path-based scheduler. MulTreePrio is promising and in future works, it will be integrated into a task-based runtime system and tested in real-life scenarios