Suppose T,S are bounded linear operators on a complex Hilbert space. We show that the Davis-Wielandt radius dw(·) satisfies the following inequalities From the third inequality we obtain the following lower and upper bounds for the Davis-Wielandt radius dw(T) of the operator T: Further, we develop several new lower and upper bounds for the Davis-Wielandt radius of the operator T which improve the existing ones. Application of these bounds are also provided. Mathematics subject classification (2020): 47A12, 47A30, 15A60, 47A50.