Let A be a positive operator on a complex Hilbert space H. Inequalities are presented concerning upper and lower bounds for A-numerical radius of operators, which improve on and generalize the existing ones, studied recently in [A. Zamani. A-Numerical radius inequalities for semi-Hilbertian space operators. Linear Algebra Appl., 578:159–183, 2019.]. Also, some inequalities are obtained for B-numerical radius of 2 × 2 operator matrices, where B is the 2 × 2 diagonal operator matrix whose diagonal entries are A. Further, upper bounds are obtained for A-numerical radius for product of operators, which improve on the existing bounds.