A single palladium (Pd) atom embedded in a high curvature defective carbon nanocone (Pd/dCNC) is investigated for formic acid (FA) decompositions using DFT calculations. We used Pd/dCNC as the catalyst for either trans-FA or cis-FA decomposition. FA is stably adsorbed on Pd/dCNC with very high adsorption energy compared to the Pd/dG surface. For the reaction mechanisms, the preferable FA dehydrogenation mechanisms proceed via the formate pathway, with a rate-determining step of only 0.50 eV (trans-FA) and 0.54 eV (cis-FA), which are less than that on active Pd (111) catalysts. The rate of hydrogen (H₂) production is dependent on the FA concentration. The active neighboring C atom plays a significant role in facilitating FA dehydrogenation into H₂. The side reaction producing CO and H₂O via the formyl or carboxyl pathway cannot occur on Pd/dCNC due to a high energy-barrier and low production rate obtained by microkinetic simulations. Thus, our proposed catalysts effectively provide excellent activity and selectivity for FA dehydrogenation into H₂.