In this study, we employ equilibrium molecular dynamics (EMD) simulation to explore the viscosity of hydrogen molecules (H2) when subjected to extreme confinement within a nanochannel made by graphene sheets. We show that the viscosity of confined H2 and, therefore, its flow rate are deeply affected by layered structure of H2 when the nanochannel height (h) becomes less than 20Å. At these heights, we observe a substantial increase in viscosity, ranging from 8 to 55 µPa.s as the h decreases from 20 to 6 Å. To this end, we investigate the impact of structural behavior of H2, the height of nanochannel, the number of H2 molecules (N), and system temperature on the viscosity. Our findings reveal a notable tendency of H2 molecules to adhere to the nanochannel wall, resulting in the formation of a densely packed layer near the wall. Additionally, our observations reveal a robust correlation between the density near the wall and the viscosity. Also, increasing the h, while keeping the N constant, leads to a noticeable decrease in viscosity. Moreover, we investigate the influence of temperature on the viscosity and demonstrate that higher temperatures enhance viscosity making more collisions of molecules to the nanochannel wall and between molecules. Furthermore, we find that viscosity increases linearly with the N due to more collision between the molecules. Exploring the behavior of hydrogen in confined environments provides valuable insights into its transport properties and its potential for applications in the industry.