Let H be a complex Hilbert space and let A be a positive operator on H. We obtain new bounds for the A-numerical radius of operators in semi-Hilbertian space BA(H) that generalize and improve on the existing ones. Further, we estimate an upper bound for the A-operator seminorm of 2 × 2 operator matrices, where A=diag(A,A). The bound obtained here generalizes the earlier related bound.