By developing Buzano type inequalities in semi-Hilbertian spaces, we obtain several A0-numerical radius inequalities for 2×2 block matrices, where A0=A00A is a 2×2 diagonal block matrix, whose each diagonal entry is a positive bounded linear operator A on a complex Hilbert space. These inequalities improve and generalize some previously related inequalities. We also deduce several improved A-numerical radius inequalities for semi-Hilbertian space operators.