In this work, three-dimensional numerical simulations of acoustically excited flow through a millimeter-size circular orifice are conducted to assess its noise damping performance, with particular emphasis on applying the lattice Boltzmann method (LBM) as an alternative computational aeroacoustics tool. The model is intended to solve the discrete lattice Boltzmann equation (LBE) by using the pseudo-particle based technique. The LBE controls the particles associated with collision and propagation over a discrete lattice mesh. Flow variables such as pressure, density, momentum, and internal energy are determined by performing a local integration of the particle distribution at each time step. This is different from the conventional numerical investigation attempting to solve Navier-Stokes (NS) equations by using high order finite-difference or finite-volume methods. Compared with the conventional NS solvers, one of the main advantages of LBM may be a reduced computational cost. Unlike frequency domain simulations, the present investigation is conducted in time domain, and the orifice damping behavior is quantified over a broad frequency range at a time by forcing an oscillating flow with multiple tones. Comparing the numerical results with those obtained from the theoretical models, large eddy simulation, and experimental measurements, good agreement is observed.