For Bernstein operators, we get the strong converse inequalities. Such inequalities have been proved by Ditzian Z., Ivanov K. G., Totik V. and Li Song with different methods. But these results are only normal estimates (with A = 1), the classical one (with A = 0) is not included. In this paper, we introduce the k-functional and extend the preuious results to a larger case 0< λ<1.