he Randic index R(G) of graph G is defined as R(G)=〖DD(X〗(x,y)∈E(G)〖DD)〗〖JB(［〗d(x)d(y)〖JB)］〗-〖SX(〗1〖〗2〖SX)〗. The Randic index is an important index in molecular topology. There is a good correlation between physical and chemical properties of certain substance and Randic index of its molecular structure. Randic index is used to find the minimum and second minimum R-values in (pertinently chosen) classes of graphs. Unicyclic graph with minimum Randic index is S+n, on the basis of which, this paper gives the second minimum Randic index of unicyclic graphs G*n .