The axisymmetric multiple-relaxation-time lattice Boltzmann (LB) method is used to study the acoustic levitation of a rigid disk sample in a closed cylindrical resonant chamber. The simulation results show that the resonant cavity length L is equal to 0.499λ for (001) mode, and the resonance shift δL is approximately equal to-0.9 with a disk sample located in the chamber center, which accord with the analytical results derived from linear acoustics. The LB method naturally includes the viscosity and resonance shift during the simulation of acoustic levitation force on the disk sample, which gives the results not only consistent with the theory in magnitude, but also coherent with the experiments in more details. Some of the nonlinear effects associated with acoustic levitation, such as waveform distortion, acoustic streaming, and radiation pressure, are also revealed by the LB simulation.