The problem of scheduling dependent tasks (DAG) is an important version of scheduling, to efficiently exploit the computational capabilities of grid systems. The problem of scheduling tasks of a graph onto a set of different machines is an NP Complete problem. As a result, a number of heuristic and meta-heuristic approaches are used over the years due to their ability of providing high quality solutions with reasonable computation time. Discrete Particle Swarm Optimization is one such meta-heuristic used for solving the discrete problem of grid scheduling, but this method converge to sub optimal solutions due to premature convergence. To deal with premature convergence, in this paper we proposed the design and implementation of hierarchical discrete particle swarm optimization (H-DPSO) for dependent task scheduling in grid environment. In H-DPSO particles are arranged in dynamic hierarchy where good particles lying above in hierarchy are having larger influence on the swarm. We consider the bi-objective version of problem to minimize makespan and total cost simultaneously as the optimization criteria. The H-DPSO based scheduler was evaluated under different application task graphs. Simulation analysis manifests that H-DPSO based scheduling is highly viable and effective approach for grid computing.