Using molecular dynamics simulations, we find an in-plane negative Poisson's ratio intrinsically existing in the graphene-based three-dimensional (3D) carbon foams (CFs) when they are compressed uniaxially. Our study shows that the negative Poisson's ratio in the present CFs is attributed to their unique molecular structures and triggered by the buckling of the CF structures. This mechanism makes the negative Poisson's ratio of CFs strongly depend on their cell length, which offers us an efficient means to tune the negative Poisson's ratio in nanomaterials. Moreover, as the buckling modes of CFs are topographically different when they are compressed in different directions, their negative Poisson's ratio is found to be strongly anisotropic, which is in contrast to the isotropic positive Poisson's ratio observed in CFs prior to buckling. The discovery of the intrinsic negative Poisson's ratio in 3D CFs will significantly expand the family of auxetic nanomaterials. Meanwhile, the mechanism of nano-auxetics proposed here may open up a door to manufacture new auxetic materials on the nanoscale.