Based on the first-principle, we optimize all geometric structures of (TM)4 clusters, calculate the energy, frequency and magnetism of (TM)4 clusters by using the local spin density approximation(LSDA) and generalized gradient approximation(GGA) density functional theory. We confirm the ground-state structures of (TM)4 clusters, study their magnetism, binding energy and average interatomic distance systematically, and find that in the 3d series (TM)4 clusters, the local magnetic moment of Mn4 cluster is the largest, that of the V4 cluster is the weakest. Except that the Cr4 cluster in LSDA and GGA shows anti-ferromagnetic coupling，and the V4 cluster in GGA shows also anti-ferromagnetic coupling, other clusters all show ferromagnetic coupling.