Highly efficient and durable anode electrocatalysts are the key to boost the performance of direct organic-molecule fuel cells (DOMFCs), yet there are still many challenges need to be solved. The PdPt alloy nanocrystals have been regarded as the most promising anode catalysts of DOMFCs, and the further improvement of their catalytic performance has attracted much attention. The effective routes includes tailoring the surface structure and optimizing the alloy composition of PdPt nanocatalysts. The high-index faceted structures possess high density of terraces and atomic steps which are efficient for electrooxidation reactions of small organic-molecule fuels, such as formic acid and ethanol. In particular, electrochemically-controlled synthesis methods present unique advantages in achieving such high-index faceted nanostructures. The current paper reports a direct electrodeposition of PdPt concave nanocubes on carbon paper (denoted as PdPt-CNC/CP). The prepared PdPt-CNC/CP has high-index faceted surface structures varying from {610} to {830}. When served as electrocatalysts, the PdPt-CNC/CP brings in outstanding mass specific activity and durability towards both formic acid oxidation reaction (FAOR) and ethanol oxidation reaction (EOR). More importantly, the selectivity of complete oxidation pathway through the cleavage of C-C bond on PdPt-CNC/CP during EOR in alkaline solution has been confirmed through NMR analysis. Based on the convenient method of direct electrodeposition of PdPt concave nanocubes on carbon paper and their excellent catalytic activity and durability, the PdPt-CNC/CP catalysts have potential advantages in being used as catalyst layers directly for membrane electrode assembly (MEA) in fuel cells, due to the reduced catalyst loading and simplified assembly process in comparison with traditional preparation procedure.