The excellent multi-functional properties of carbon nanotube (CNT) and graphene have enabled them as appealing building blocks to construct 3D carbon-based nanomaterials or nanostructures. The recently reported graphene nanotube hybrid structure (GNHS) is one of the representatives of such nanostructures. This work investigated the relationships between the mechanical properties of the GNHS and its structure basing on large-scale molecular dynamics simulations. It is found that increasing the length of the constituent CNTs, the GNHS will have a higher Young’s modulus and yield strength. Whereas, no strong correlation is found between the number of graphene layers and Young’s modulus and yield strength, though more graphene layers intends to lead to a higher yield strain. In the meanwhile, the presences of multi-wall CNTs are found to greatly strengthen the hybrid structure. Generally, the hybrid structures exhibit a brittle behavior and the failure initiates from the connecting regions between CNT and graphene. More interestingly, affluent formations of monoatomic chains and rings are found at the fracture region. This study provides an in-depth understanding of the mechanical performance of the GNHSs while varying their structures, which will shed lights on the design and also the applications of the carbon-based nanostructures.