Let G = (V,E), V = {v1,v2, . . . ,vn}, E = {e1,e2, . . . ,em}, be a simple connected graph with the vertex degree sequence Δ = d1 ≥ d2 ≥ · · · ≥ dn =δ > 0, di = d(vi). The zeroth–order general Randi´c index, 0Rα (G), of a connected graph G, is defined as 0Rα (G) = Σni=1 dα i .A linear combination of 0Rα (G) of the form irr(α)(G) = 0Rα+1(G)− 2m n 0Rα (G), α ≥ 0, can be considered as an irregularity measure of a graph since irr(α)(G) = 0 if and only if G is a regular graph, and irr(α)(G) > 0 otherwise. In this paper we consider a linear combination irr(α)(G)− 2m n irr(α−1)(G), for α ≥ 1, which can be also considered as irregularity measure of graph, and determine its bounds.