In this paper, we define a non-Newtonian superposition operator P-N(f) where f : N x R(N)(alpha) -> R(N)(beta) by P-N(f) (x) = (f (k, x(k)))(k=1)(infinity) for every non-Newtonian real sequence x = (x(k)). Chew and Lee  have characterized P-f : l(p) -> l(1) and P-f : c(0) -> l(1) for 1 <= p < infinity. The purpose of this paper is to generalize these works respect to the non-Newtonian calculus. We characterize P-N(f) : l(infinity)(N) -> l(1)(N), P-N(f) : c(0)(N) -> l(1)(N) and P-N(f) : l(p)(N) -> l(1)(N) respectively. Then we show that such P-N(f) : l(infinity)(N) -> l(1)(N) is *-continuous if and only if f(k, .) is *-continuous for every k is an element of N.