Molybdenum disulfide (MoS2) is considered as a promising noble-metal-free electrocatalyst for the Hydrogen Evolution Reaction (HER). However, to effectively employ such material in the HER process, the corresponding electrocatalytic activity should be comparable or even higher than that of Pt-based materials. Thus, efforts in structural design of MoS2 electrocatalyst should be taken to enhance the respective physico-chemical properties, particularly, the electronic properties. Indeed, no report has yet appeared about the possibility of an HER electrocatalytic association between the MoS2 and carbon nanotubes (CNT). Hence, this paper investigates the synergistic electrocatalytic activity of MoS2/ CNT heterostructure for HER by Density Functional Theory simulations. The characteristics of the heterostructure, including density of states, binding energies, charge transfer, bandgap structure and minimum-energy path for the HER process were discussed. It was found that regardless of its configuration, CNT is bound to MoS2 with an atomic interlayer gap of 3.37 Å and binding energy of 0.467 eV per carbon atom, suggesting a weak interaction between CNT and MoS2. In addition, the energy barrier of HER process was calculated lower in MoS2/CNT, 0.024 eV, than in the MoS2 monolayer, 0.067 eV. Thus, the study elaborately predicts that the proposed heterostructure improves the intrinsic electrocatalytic activity of MoS2.