The balance between exploration and exploitation is critical to the performance of a Meta-heuristic optimization method. At different stages, a proper tradeoff between exploration and exploitation can drive the search process towards better performance. This paper develops a multi-objective grasshopper optimization algorithm (MOGOA) with a new proposed framework called the Multi-group and Co-evolution Framework which can archive a fine balance between exploration and exploitation. For the purpose, a grouping mechanism and a co-evolution mechanism are designed and integrated into the framework for ameliorating the convergence and the diversity of multi-objective optimization solutions and keeping the exploration and exploitation of swarm intelligence algorithm in balance. The grouping mechanism is employed to improve the diversity of search agents for increasing coverage of search space. The co-evolution mechanism is used to improve the convergence to the true Pareto optimal front by the interaction of search agents. Quantitative and qualitative outcomes prove that the framework prominently ameliorate the convergence accuracy and convergence speed of MOGOA. The performance of the presented algorithm has been benchmarked by several standard test functions, such as CEC2009, ZDT and DTLZ. The diversity and convergence of the obtained multi-objective optimization solutions are quantitatively and qualitatively compared with the original MOGOA by using two performance indicators (GD and IGD). The results on test suits show that the diversity and convergence of the obtained solutions are significantly improved. On several test functions, some statistical indicators are more than doubled. The validity of the results has been verified by the Wilcoxon rank-sum test. Keywords: multi-objective optimization; meta-heuristics; swam intelligence algorithm; grasshopper optimization algorithm