Liquid organic hydrogen carrier (LOHC) is one of the advantageous hydrogen storage technologies, which store hydrogen through a chemical bond in liquid organic compounds. We previously developed a promising LOHC material, 2-[N-methylbenzyl]pyridine (MBP). However, the mechanism and catalytic behavior for the dehydrogenation of dodecahydro-MBP (H-12-MBP) on the catalysts are not still clear. For the fundamental understanding of H-12-MBP dehydrogenation, we focused on the two main fragments of H-12-MBP that are 1,2-dimethyl cyclohexane (DCH) and 2-methyl piperidine (MPD). Density functional theory (DFT) calculations were performed to investigate their catalytic dehydrogenation on Pd(111) and Pt(111). In order to compare the catalytic activities, the reaction energy profiles for DCH and MPD on both surfaces were calculated. By identifying the rate-determining steps, it was found that Pd had higher (lower) catalytic activity for MPD (DCH) than Pt. The different dehydrogenation sequences on Pd(111) and Pt(111) due to the different preference of bond formation for pi and sigma, respectively can be one of the origins for the different catalytic activities between the two catalysts.