The hybridization of carbon-based nanomaterials (i.e CNTs, fullerenes and graphene) via chemical bonding provides a preferable way to maximize and control their exceptional properties. In line with this understanding, in this study, the design and analysis of new porous graphene-carbon nanotube (G-CNT) hybrid structures obtained by organizing graphene nanoribbons around the CNT units in three different geometric patterns (i.e. square, hexagon, diamond) is presented. With this motivation, after examining the thermodynamic feasibility of the nanostructures, the mechanical and thermal properties are examined by considering the effects of different pattern geometries through classical molecular dynamics simulations. In addition, in order to increase the compressive strength and energy absorption capacity of G-CNT structures, fullerenes are employed as filler units within the cells. Simulation results show that the proposed G-CNT structures have remarkable thermal and mechanical characteristics, which can be modified by the geometric arrangement of CNTs and graphene nanoribbons as well as by the filler agents. Controllability of the thermal conductivity and mechanical strength is promising for different application fields where their ultra-lightweight plays an eminent role.