In this paper we construct a new operator ${H^{(N,B)}_{n,r}}(f;z)$ by means of the partial sums ${S^{(N,B)}_{n}}(f;z)$ of Neumann-Bessel series. The operator converges uniformly to any fixed continuous function $f(z)$ on the unit circle $\mid z \mid=1 $ and has the best approximation order for $f(z)$ on $\mid z\mid=1.$
