In the late three decades, grid computing has emerged as a new field providing a high computing performance to solve larger scale computational demands. Because Directed Acyclic Graph (DAG) application scheduling in a distributed environment is a NP-Complete problem, meta-heuristics are introduced to solve this issue. In this paper, we propose to hybridize two well-known heuristics. The first one is the Heterogeneous Earliest Finish Time (HEFT) heu-ristic which determines a static scheduling for a DAG in a heterogeneous environment. The second one is Particle Swarm Optimization (PSO) which is a sto-chastic meta-heuristic used to solve optimization problems. This hybridization aims to minimize the makespan (i.e., overall competition time) of all the tasks within the DAG. The experimental results that have been conducted under hy-bridization show that this approach improves the scheduling in terms of completion time compared to existing algorithms such as HEFT.