Let) A be a positive (semidefinite) operator on a complex Hilbert space H and let (Formula presented). We obtain upper and lower bounds for the A-Davis-Wielandt radius of semiOA Hilbertian space operators, which generalize and improve on the existing ones. Further, we derive upper bounds for the A-Davis-Wielandt radius of the sum of the product of semi-Hilbertian space operators. We also obtain upper bounds for the A-Davis-Wielandt radius of 2×2 operator matrices. (Finally,) we determine the exact value for the A-Davis-Wielandt radius of two operator matrices (Formula presented) and (Formula presented), where X is a semi-Hilbertian space operator, and I, O are OO OO the identity operator, the zero operator on H, respectively.