Grid systems integrate distributed resources to form self-organization and self-management autonomies. Recently, for large-scale computation requirement, the collaboration of different grid systems is one of the hot research topics. In this paper, we propose a meta-grid framework, called G2G framework, to harmonize autonomic grids for realizing the federation of different grids. The G2G framework is a decentralized management framework on top of existing autonomic grid systems. It adopts a super-peer network to coordinate distributed grid systems. A super-peer overlay network is constructed for the communication among super-peers in different grid systems. The contribution of this study is to propose a G2G framework for the Grid-to-Grid federation and to implement a preliminary system. Experimental results show that the proposed meta-grid framework could improve the system performance in the G2G system.