Let A =(A00A) be a 2 × 2 diagonal operator matrix whose each diagonal entry is a positive bounded linear operator A acting on a complex Hilbert space H. Let T, S and R be bounded linear operators on H admitting A-adjoints, where T and R are A-positive. By considering an A-positive 2×2 operator matrix (TSS#AR), we develop several upper bounds for the A-numerical radius of S. Applying these upper bounds we obtain new A-numerical radius bounds for the product and the sum of arbitrary operators which admit A-adjoints. Related other inequalities are also derived.