Summary: This paper designs the consensus based formation control laws for multi-agent systems defined on Lie groups. The specific results are illustrated on \(SE(2)\) and \(SE(3)\) (the special Euclidean groups of rigid body motions and each of which shares the geometric structure of a Lie group). The paper develops the control laws for the problem concerned under the assumption that the communication topologies of the multi-agent systems are spanning-tree-shaped, ring-shaped and complete, respectively. At last, several examples are included in the numerical simulations to verify the theoretical results.