Concave metallic nanocrystals with a high density of low-coordinated atoms on the surface are essential for the realization of unique catalytic properties. Herein, mesoporous palladium nanocrystals (MPNs) that possess various degrees of curvature are successfully synthesized following an approach that relies on a facile polymeric micelle assembly approach. The as-prepared MPNs exhibit larger surface areas compared to conventional Pd nanocrystals and their nonporous counterparts. The MPNs display enhanced electrocatalytic activity for ethanol oxidation when compared to state-of-the-art commercial palladium black and conventional palladium nanocubes used as catalysts. Interestingly, as the degree of curvature increases, the surface-area-normalized activity also increases, demonstrating that the curvature of MPNs and the presence of high-index facets are crucial considerations for the design of electrocatalysts.