The mechanical response of graphene foams (GrFs) can be enhanced by both short crosslinkers (e.g. C-C bond) and long carbon nanotubes (CNTs) in experiments; however, the underlying mechanism is still unclear. Here, a coarse-grained molecular dynamics method is used to study the mechanical response and microscopic mechanism of GrF interconnected by both short crosslinkers and long CNTs (named CNT bonded GrF, CbGrF) under tension and compression, and the effect of the properties of graphene and CNTs on the mechanical properties of CbGrF is also investigated. Compared with short bonds, long CNTs play a reinforcing role at a larger tensile strain, leading to larger tensile strength and toughness. Under compression, the sliding and rotation of graphene sheets in CbGrF are prevented by long CNTs, resulting in higher compressive stiffness than that of pure GrFs. Furthermore, the tensile and compressive moduli increase by more than 300% with increasing thickness of graphene sheets from 1 to 9 layers; they increase by no more than 50% as the CNT bending stiffness increases and are almost independent of the stretching stiffness of CNTs. These results should be helpful for understanding the tunability of GrFs using both short and long crosslinkers and guiding the preparation of advanced GrF-based composites.