Grid computing emerged as a powerful computing domain for running large-scale parallel applications. Scheduling computationally intensive parallel applications such as scientific, commercial etc., computational grids is a NP-complete problem. Many researchers have proposed several task scheduling algorithms on grids based on formulating and solving it as an optimization problem with different objective functions such as makespan, cost, energy etc. Further to address the requirements/demands/needs of the users (lesser cost, lower latency etc.) and grid service providers (high utilization and high profitability), a task scheduler needs to be designed based on solving a multi-objective optimization problem due to several trade-offs among the objective functions. In this direction, we propose an efficient multi-objective task scheduling framework to schedule computationally intensive tasks on heterogeneous grid networks. This framework minimizes turnaround time, communication, and execution costs while maximizing grid utilization. We evaluated the performance of our proposed algorithm through experiments conducted on standard, random, and scientific task graphs using the GridSim simulator.