The ground-state geometries of Rh_n(n=2~20) clusters are calculated with a TB many-body potential in the Genetic Algorithm(GA). Based on the optimized geometries, we calculate the average bond length(R), average coordination number(CN), average binding energy E_b per atom. The average magnetic moment per atom μ_n and the average total density of states(DOS) of Rh_n(n=15,17,18,19) clusters are calculated in a self-consistent tight-binding model considering 4 d, 5 s, 5 p valence electrons with both global and local neutrality. Our result reveals relations between structure and electronic and magnetic properties of small Rh clusters.