The composites made from cubic silicon carbide (3C-SiC), as a matrix, and carbon nanotubes (CNTs), as reinforcements, have a wide range of applications in the industry because of their unique mechanical properties. However, to make effective and efficient composites of 3C-SiC/CNTs, the manner composition of 3C-SiC and CNTs and their volume fraction are among the biggest challenges. Therefore, in this study, to clarify the effects of different volume fractions of various CNT structures on 3C-SiC, continuous fiber composites of 3C-SiC/CNTs are investigated via the molecular dynamics (MD) method. The utilized reinforcements include Single Wall Carbon Nanotubes (SWCNT), Ropes Single Wall Carbon Nanotubes (RSWCNTs), and Multi-Walled Carbon Nanotubes (MWCNTs). The results reveal that the CNTs in the 3C-SiC/CNTs under axial stress are able to bear the most stress and yield before the 3C-SiC, the values of the Young's modulus of the 3C-SiC/SWCNTs, 3C-SiC/RSWCNTs, and 3C-SiC/MWCNTs boost as the chiral indices, the number of ropes, and the number of layers increase, respectively, and the 3C-SiC/CNTs, as continuous fiber composites, have the reinforced Young's modulus and the weakened fracture stress. In addition, among this type of composites, the 3C-SiC/MWCNTs with almost the same weight have the greatest value of the Young's Modulus; thus, they are the most appropriate composites for the industrial applications with high mechanical stiffness.