Abstract: In this paper a new operator G_n(f;x) is constrcucted by means of the linear combination of Bernstein and Grünwald operators on the basis of taking the zeros of the first kind of Chebyshev polynomial of degreen as the interpolating nodes. G_n(f;x) converges to the f(x)∈C^j_［-1,1］, 0≤j≤9 on ［-1,1］ uniformly and has the best approximation order if the function f(x)∈C^j_［-1,1］, 0≤ j≤9. The saturation order is 1/n¹⁰.

Key words: Bernstein operator, Grünwald operator, convergence order, saturation order