On the basis of density-functional theory and all-electron numerical basis set, 20 stable isomers of Fe3C2 cluster are found through optimization calculations and frequency analysis from 108 initial structures. A nonplanar C-s structure with nonet spin multiplicity and 482.978 kcal/mol of binding energy is found as the candidate of global minimum geometry of Fe3C2 cluster. The binding energies, the energy gaps between the highest occupied molecular orbital and the lowest unoccupied molecular orbital, and the magnetic moments of all the isomers are reported. The relationship between the molecular properties and geometrical structures is also investigated.