Abstract: With the rapid development of network technology, Grid Computing has emerged for satisfying the increasing demand of the computing power of scientific computing community. Grid facilitates global computing infrastructure for user to consume the services over the network. To optimize the workflow grid execution, a robust multi-objective scheduling algorithm is needed. In this paper, we considered three conflicting objectives like execution time (makespan), total cost and reliability. We propose a multi-objective scheduling algorithm, using R-NSGA-II approach based on evolutionary computing paradigm. Simulation results shows that the proposed algorithm generates multiple scheduling solutions near the Pareto optimal front with small computation overhead. In this work, we proposed the use of epsilon dominance based MOEA approach for the purpose of solving workflow scheduling problems in Grid. In one scheduling problem, we addressed two major conflicting objectives called make span and cost.