Free and supported platinum concave nanocubes exposing {110} facets have been prepared by a wet-chemistry route and used as catalysts for the selective hydrogenation of cinnamaldehyde. The nanocubes were directly grown on few layer graphene support in the presence of octadecylamine as a stabilizing agent. Immobilization improves both activity and selectivity towards the desired unsaturated alcohol. The presence of the organic stabilizer guarantees the stability of the nanoparticle morphology and influences the catalyst performances. While the activity is favored by small nanoparticles and low ligand contents, the selectivity to the unsaturated alcohol is favored by high ligand contents, most likely due to steric effects that favor adsorption through the C=O moiety. Apart from stabilizing the nanocubes, the support interacts with the long chain amine ligand, behaving as a ligand reservoir. Thus, an equilibrium is established between the ligand interacting with the nanoparticles, the free ligand in solution, and the ligand interacting with the support. Ligand redistribution during the catalytic reaction assures a good compromise between activity and selectivity even after three recycling tests. While a direct comparison with other catalysts is not straightforward, the FLG-supported concave nanocubes presented outstanding activity, and selectivity to cinnamyl alcohol higher than 80%.