In this paper, a bimetallic sensor based on graphene-hexagonal boron nitride (hBN) heterostructure is theoretically studied. The sensitivity of the sensor can be improved by enhancing the Goos–Hänchen (GH) shift in the infrared band. The theoretical results show that adjusting the Fermi level, the number of graphene layers and the thickness of hBN, a GH shift of 182.09 λ can be obtained. Moreover, sensitivity of 2.02 × 105 λ/RIU can be achieved with monolayer graphene, the thickness of gold layer is 20 nm, silver layer is 15 nm, and the hBN thickness of 492 nm. This heterogeneous infrared sensor has the advantages of high sensitivity and strong stability. The research results will provide a theoretical basis for the design of a new high-sensitivity infrared band sensor.