The present work aims to examine the metamaterial vibrational behavior of circular few-layer graphene sheets under layerwise tension forces. For this objective, a simplified three-membrane model is developed to simulate flexural vibration of tensioned circular few-layer graphene sheets, in which tensioned top and bottom layers are modeled as two elastic membranes while all less-tensioned or tension-free inner layers together are treated as a single membrane, and the three membranes are coupled through the van der Waals interaction between adjacent layers. Our results show that when the two outermost layers are highly tensioned but the inner layers are free of tension, circular few-layer graphene sheets exhibit negative effective mass within a certain terahertz frequency range. Moreover, such few-layer graphene sheets with negative effective mass demonstrate remarkable vibration isolation and vibration suppression. This research broadens our perspectives for designing and analyzing graphene-based metamaterials and resonators and could find potential application in nanoelectromechanical systems.