We theoretically perform a comprehensive analysis about the influences of the space-inversion symmetry breaking in graphene-based materials on the Andreev reflections (AR) in the normalmetal/superconductor (NS) and NSN heterojunctions. It is found that in the NS junction, the AR can be suppressed or be enhanced by the enhancement of space-inversion symmetry breaking, depending on the relationship among the coherence parameters. Following this result, the AR properties in the NSN structure are evaluated. It is readily observed that the local AR can be weakened for low spaceinversion symmetry breaking, and can be enhanced for high space-inversion symmetry breaking. Alternatively, the efficiency of the crossed AR can be improved to a great degree, with the increase of space-inversion symmetry breaking. One can therefore understand the special role of space-inversion symmetry in modulating the AR, especially for the enhancement of crossed AR. ferromagnetic leads are introduced to couple to the QDs, spin-polarized Andreev transport can be observed [34].On the other hand, graphene-based Cooper pair splitters have received a lot of attentions, after the successful fabrication of graphene. Graphene has the advantage of the controllability of its-based mesoscopic circuits, and it can be superconducting by proximity to a superconductor on top of it [35][36][37]. This has attracted vast studies in the electronic transport through the NS heterostructures based on graphene [38][39][40][41]. It is also known that graphene has the linear dispersion relation and the conduction and valence bands touch each other at the Dirac point, making it a gapless semiconductor. Hence in graphene, the carrier type (electron: n-type; hole: p-type) and its density can be easily tuned in a controllable manner by local electrostatic gates or chemical doping. Many groups have demonstrated that the two-dimensional crystals, e.g. graphene, are possible areas for CAR processes where the magnitude of the CAR conductance can be enhanced in NSN hybrid structures. By building the NSN structure with the n-type and p-type graphene coupled to the superconducting part, channels for the electron transmission (ET) and local Andreev reflection (LAR) processes have been found to be seriously suppressed, leading to the enhancement of CAR process [42]. Other researches try to improve the CAR efficiency by proposing a graphene-based NSN spin valve [43]. This shows a spin-switch effect between pure CAR process and pure ET through the reverse of the magnetization direction in the ferromagnetic layers. Besides, a pure CAR process has been observed in a magnetized zigzag graphene nanoribbon junction with an even zigzag chain number [44].It is well known that besides the physical real spin index in graphene, one additional intrinsic degree of freedom also affects the properties of graphene, due to the existence of two types of carbon atoms (labeled as A and B) in the honeycomb lattice of graphene. When A and B atoms are different in energy, the space-inversion symmetry ...