We used density functional theory (DFT) to investigate hydrogen adsorption and diffusion on platinum-decorated carbon nanocones (Pt-CNCs). The curvature presented in the conical section of CNC materials affects the Pt binding stability. The role of Pt atoms as an active catalyst for H2 adsorption and dissociation has been investigated in perfect Pt-4CNC and defect Pt-v4CNC systems. Then, the spillover mechanism of dissociated hydrogen atoms in Pt-v4CNC is explored via two reaction steps: (i) H-migration from Pt to carbon atoms and (ii) H-diffusion via the C-C route throughout the CNC surface. Our results show that the presence of the hydrogen atom on the Pt catalyst can efficiently induce the H-diffusion process through the C-C surface, and the Pt-H bond significantly facilitates the H-migration from C-H bonds near to the active Pt catalyst to the adjacent carbon atom with an energy barrier <0.5 eV under ambient conditions. Altogether, the theoretical results support the concept of the spillover mechanism as a key process for enhancing the hydrogen storage capacity of metal-decorated CNCs. These results improve our understanding about the hydrogen spillover mechanism and the catalytic reactions which are very important for the development of highly efficient hydrogen storage materials.