Based on Euler-Bernoulli beam theory, Hamilton’s principle and Galerkin method, the second-order nonlinear ordinary differential dynamical equation was derived for the cantilever metal foam sandwich beam under transverse loading. The effect of damping on the vibration response of the metal foam sandwich beam was investigated for the cases of different frequencies and amplitudes of the transverse loading. It is shown that the chaotic vibration of the sandwich beam can be suppressed effectively by the damping performance of metal foam.