The purpose of the paper is to determine fine spectrum of newly introduced operator Δν on the sequence space c0. The operator Δν on c0 is defined by Δνχ = (νnχn - νn-1χn-1)n=0∞ with χ-1 = 0, where ν = (νk) is either constant or strictly decreasing sequence of positive real numbers such that lim νk = L > 0 and sup νk ≤ 2L. In this paper, it is shown that spectrum (These equations cannot be represented into ASCII text), the point spectrum σp(Δν,c0) = ϕ if ν is a constant and σp(Δν,c0) = {νn} if ν is a strictly decreasing sequence. We have also obtained the results on continuous spectrum σc(Δν,c0), residual spectrum σr(Δν,c0) and fine spectrum of the operator Δν on c0. [ABSTRACT FROM AUTHOR]