In this study, Brinkman penalization method (BPM) is extended for prediction of acoustic scattering from complex geometries. The main idea of the BPM is to model the solid obstacle as a porous material with zero porosity and permeability. With the aim of increasing the spatial accuracy at the immersed boundaries, computation is carried out on the boundary-fitted Cartesian-like grid with a high-order compact scheme combined with one-side differencing/filtering technique at the boundaries, while a slip boundary condition at the wall is imposed by introducing the 'anisotropic' penalization terms to the momentum equations. Several test cases are considered to demonstrate the accuracy, robustness and feasibility of the BPM. Numerical results are in excellent agreement with the analytic solutions for single and two cylinder scattering problems. The present BPM is then used to solve the acoustic scattering from a three-element high-lift wing (30P30N model).