Wrinkles in graphene with desirable morphology have practical significance for electronic applications. Here we carry out a systematic molecular dynamics study of the wrinkling instability of graphene on substrate-supported nanoparticles (NPs). At a large NP dispersion distance, a monolayer graphene adheres to the substrate and bulges out locally to wrap around individual NPs, forming isolated dome-shaped protrusions. At a small NP dispersion distance, tunneling wrinkles form in graphene to bridge the NP-induced protrusions. A critical NP dispersion distance for the onset of tunneling wrinkle instability of graphene is determined as a function of the NP size. The prediction from the modeling study agrees well with recent experimental observations. Results from the present study offer further insights into the formation of desirable wrinkles in graphene deposited on a substrate with engineered protrusions and, thus, can potentially enable novel design of graphene-based electronics.