This paper presents an order-reduction-iteration approach for vibration analysis of viscoelastically damped sandwiches. The damping property of all kinds of viscoelastically damped sandwich structures can be predicted by the approach that consists of two steps, i.e., the first-order asymptotic solution of the non-linear real eigenequation and the order-reduction-iteration of the non-linear complex eigenequation. The experimental results for sandwich beams agree well with the numerical ones in this paper.