Based on the traditional adaptive integral method(AIM), a fast method called array AIM is proposed to accelerate the scattering calculation of the finite periodic array and the sparse array. On one hand, this method could eliminate the idle grids through the utilization of 5-level block-Toeplitz matrix. Furthermore, the procedure of near correction is eliminated by applying the zeros shielding technique. On the other hand, the block Jacobi preconditioning technique is used to improve the iterative convergence, and the technique of wave path difference compensation is applied to accelerate the post-processing. The numerical results show that the proposed method not only possesses good accuracy, but also has much less cost both in time and memory, in comparison with the traditional AIM. Moreover, this method could be applied to solve the scattering problems for the finite periodic array, as well as the sparse array.