A saturated star-shaped polystyrene-b-poly(ethylene-co-propylene block copolymer, (SEP)(star), was synthesized for use as a viscosity index improver in lubricants. Polystyrene-b-polyisoprene arms were first made anionically, followed by a linking reaction at the optimum temperature of 60 degreesC with divinylbenzene. The resulting star-shaped (SI)(star) was hydrogenated to eliminate the double bonds on the polyisoprene segment, thus forming the star-shaped (SEP)(star). The number of arms on each molecule increased with an increase in the mol ratio of divinylbenzene to n-butyl-lithium. Increasing the arm length adversely affected the linking efficiency but caused a slight increase in the degree of branching. The T-g of the poly(ethylene-co-propylene) block was 13 degreesC higher than that of the original polyisoprene block. Compared with (SI)(star) (SEP)(star) has a thermal decomposition temperature 50 degreesC higher but independent of the arm length or the degree of branching. Viscosity measurements for (SEP)(star) revealed that intrinsic viscosity depends only on the arm length, but not on the degree of branching. Adding 1 wt % of (SEP)(star) markedly increased the viscosity index of a HN base oil. With a fixed arm length, a (SEP)(star) having a higher degree of branching increased the viscosity index more than that having a lower degree of branching. On the other hand, the viscosity index increased with an increase in the arm length when the degree of branching was fixed. The addition of 1wt% of (SEP)(star) increased the vioscosity index up to a number between 111 and 166, with the exact number depending upon its arm length and degree of branching.