Graphene plasmons are rapidly emerging as a versatile platform for manipulating light at the deep subwavelength scale. Here we show numerically that strong optical near-field forces can be generated under the illumination of mid-IR light when dielectric nanoparticles are located in the vicinity of a nanostructured graphene film. These near-field forces are attributed to the excitation of the graphene's plasmonic mode. The optical forces can generate an efficient optical trapping potential for a 10-nm-diameter dielectric particle when the light intensity is only about about 4.4 mW/μm2 and provide possibilities for a new type of plasmonic nano-tweezers. Graphene plasmonic tweezers can be potentially exploited for optical manipulation of nanometric biomolecules and particles. Moreover, the optical trapping/tweezing can be combined with biosensing and provide a versatile platform for studing biology and chemistry with mid-IR light.