In this paper, a nondestructive evaluation technique based on highly nonlinear solitary waves (HNSWs) is proposed to monitor the curing process of adhesive for composite/metal bonded structure. HNSWs are mechanical waves with high energy intensity and non-distortive nature which can form and propagate in a nonlinear system, such as a one-dimensional granular chain. In the present study, a finite element model of the one-dimensional granular chain is established with the commercial software Abaqus, to study the reflection behavior of HNSWs at the interface between the particle at the end of chain and the sample. The simulation results show that the time of flight (TOF) of the primary reflected solitary wave decreases with the stiffness of the sample increases, and the amplitude ratio (AR) between the primary reflected solitary wave and the incident solitary wave increases. An HNSWs transducer based on the one-dimensional granular chain is designed and fabricated. The relationship between the characteristic parameters of the primary reflected solitary wave (TOF and AR) and the curing time of adhesive for a composite/metal bonded structure is experimentally investigated. The experiment results suggest that the TOF decreases and the AR increases as the epoxy cures. The experimental results are in good agreement with the simulation results. This study provides a new characterization method for monitoring the curing process of adhesive for composite/metal bonded structure.