Graphene plasmons with enhanced localized electric field have been used for boosting the light-matter interaction in linear optical nano-devices. Meanwhile, graphene is an excellent nonlinear material for several third-order nonlinear processes. We present a theoretical investigation of the mechanism of plasmon-enhanced third-order nonlinearity susceptibility of graphene nanoribbons. It is demonstrated that the third-order nonlinearity susceptibility of graphene nanoribbons with excited graphene surface plasmon polaritons can be an order of magnitude larger than the intrinsic susceptibility of a continuous graphene sheet. Combining these properties with the relaxed phase matching condition due to the ultrathin graphene, we propose a novel plasmon-enhanced mid-infrared (MIR) wavelength converter with arrays of graphene nanoribbons. The wavelength of signal light is in the MIR range, which can excite the tunable surface plasmons polaritons in arrays of graphene nanoribbons. The efficiency of the converter from MIR to near-infrared wavelength can be remarkably improved by 60 times compared with a graphene sheet without graphene plasmons. This work provides a novel idea for the efficient application of graphene in nonlinear optical nano-devices. The proposed MIR wavelength converter is compact, tunable and has promising potential in graphene-based MIR detectors with high detection efficiency.