Let G = (V, E), V = {v1, v2, . . . , vn}, be a simple connected graph of order n and size m. Denote by γ+1 ≥ γ+2 ≥ · · · ≥ γ+n ≥ 0 the normalized signless Laplacian eigenvalues of G, and by σα(G) the sum of α-th powers of the normalized signless Laplacian eigenvalues of a connected graph. The paper deals with bounds of σα. Some special cases, when α = 12 and α = −1, are also considered.