Axion insulator is an exotic magnetic topological insulator with zero Chern number but a nonzero quantized Chern-Simons magnetoelectric coupling. A conclusive experimental evidence for axion insulators is still lacking due to the small signal of topological magnetoelectric effect (TME). Here we show that the dynamical magnetoelectric coupling can be induced by the emph{out-of-plane} surface magnetization dynamics in axion insulator thin films, which further generates a polarization current in the presence of an external magnetic field in the same direction. Such a current is finite in the bulk and increases as the film thickness $d$ decreases, in opposite to TME current which decreases as $d$ decreases. Remarkably, the current in thin films at magnetic resonance is at least ten times larger than that of TME, and thus may serve as a smoking gun signature for axion insulators.
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