In this paper, we define a non-Newtonian superposition operator NP f where f : N × R(N)α → R(N)β by NP f (x) = ( f (k, xk) )∞ k=1 for every non-Newtonian real sequence x = (xk). Chew and Lee [4] have characterized P f : `p → `1 and P f : c0 → `1 for 1 ≤ p < ∞ . The purpose of this paper is to generalize these works respect to the non-Newtonian calculus. We characterize NP f : `∞ (N)→ `1 (N) , NP f : c0 (N)→ `1 (N) , NP f : c (N)→ `1 (N) and NP f : `p (N)→ `1 (N), respectively. Then we show that such NP f : `∞ (N)→ `1 (N) is *-continuous if and only if f (k, .) is *-continuous for every k ∈N,