Graphene plasmon with extremely strong light confinement and tunable resonance frequency represents a promising surface-enhanced infrared absorption (SEIRA) sensing platform. However, plasmonic absorption is relatively weak (approximately 1%-9%) in monolayer graphene nanostructures, which would limit its sensitivity. Here, we theoretically propose a hybrid plasmon-metamaterial structure that can realize perfect absorption in graphene with a low carrier mobility of 1000 cm2 V-1 s-1. This structure combines a gold reflector and a gold grating to the graphene plasmon structures, which introduce interference effect and the lightning-rod effect, respectively, and largely enhance the coupling of light to graphene. The vibration signal of trace molecules can be enhanced up to 2000-fold at the hotspot of the perfect-absorption structure, enabling the SEIRA sensing to reach the molecular level. This hybrid metal-graphene structure provides a novel path to generate high sensitivity in nanoscale molecular recognition for numerous applications.