Tuning the composition and structure of alloys is significantly important to unveil their relationship between structure and functions, and thus help to design catalysts with high performance. In this work, PdPt octahedral and concave cubic nanoparticles (OH-PdPt NPs and CC-PdPt NPs) were synthesized firstly by developed electrochemical methods. EDS and XPS studies revealed that the as-synthesized PdPt NPs have similar composition both in bulk and surface. The alloy nanoparticles show surface structure dependent enhanced activity and stability for methanol, ethanol and glycerol electrooxidations (MOR, EOR and GOR). The {hk0} high-index facets enclosed CC-PdPt NPs show higher activity towards MOR and EOR which is 7.0-fold and 3.4-fold respectively higher than commercial Pt/C. However, {1 1 1} low-index facets enclosed OH-PdPt NPs show superior activity towards GOR, which is 4.5-fold higher than commercial Pt/C. The selective enhancing catalytic ability of PdPt NPs towards different alcohol electrooxidations could be attributed to the synergetic effect and modified electronic structure of Pd and Pt, as well as the important effects of surface atomic configuration. DFT calculations suggest that the higher activity of methanol and ethanol oxidation on high-index {hk0} facets is due to the faster decomposition process and lower oxidation barrier on the step sites. Nevertheless, the strong adsorption of COCHOHCO* on step sites leading to a much higher oxidation barrier, indicating the step sites of {hk0} facets are not beneficial for glycerol oxidation.