An adaptive nonlinear artificial dissipation model is presented for performing aeroacoustic computations by the high-order and high-resolution numerical schemes based on the central finite differences. An effective formalism of it is devised by combining a selective background smoothing term and a well-established nonlinear shock-capturing term which is for the temporal accuracy as well as the numerical stability. A conservative form of the selective background smoothing term is presented to keep accurate phase speeds of the propagating nonlinear waves. The nonlinear shock-capturing term that has been modeled by the second-order derivative term is combined with it to improve the resolution of discontinuities and stabilize the strong nonlinear waves. It is shown that the improved artificial dissipation model with an adaptive control constant which is independent of problem types reproduces the correct profiles and speeds of nonlinear waves, suppresses numerical oscillations near discontinuity and avoids unnecessary damping on the smooth linear acoustic waves. The feasibility and performance of the adaptive nonlinear artificial dissipation model are investigated by the applications to actual computational aeroacoustics problems.