This paper computationally investigates the RhSin(n = 1-6) clusters by using a density functional approach. Ge- ometry optimizatious of the RhSin(n = 1-6) clusters are carried out at the B3LYP level employing LanL2DZ basis sets. It presents and discusses the equilibrium geometries of the RhSin(n=1-6) clusters as well as the corresponding aver- aged binding energies, fragmentation energies, natural populations, magnetic properties, and the energy gaps between the highest occupied molecular orbital and the lowest unoccupied molecular orbital. Theoretical results show that the most stable RhSin(n=1-6) isomers keep an analogous framework of the corresponding Sin+1 clusters, the RhSi3 is the most stable cluster in RhSin(n = 1-6) isomers. Furthermore, the charges of the lowest-energy RhSin(n = 1-6) clusters transfer mainly from Si atom to Rh atom. Meanwhile, the magnetic moments of the RhSin(n = 1-6) arises from the 4d orbits of Rh atom. Finally, compared with the Sin+1 cluster, the chemical stability RhSin clusters are universally improved.