Herein, we introduce a facile strategy for the structure-controlled synthesis of one-dimensional PdCu nanocrystals via a seed-mediated approach. This developed strategy involves the synthesis of Cu nanowires with penta-twinned structure, and subsequent growth of Pd metal on Cu nanowires. The obtained one-dimensional PdCu nanocrystals are of rough surfaces and core-shell like architecture. Upon the tuning reactivity of (111) and (100) crystal faces on Cu nanowires in absence or presence of capping agent, one-dimensional PdCu nanocrystals with solid or hollow interiors (nanowires or nanotubes) can be controllably synthesized through galvanic displacement reaction, respectively. It is found that both PdCu nanowires and PdCu nanotubes exhibit better performance for oxygen reduction reaction compared with self-synthesized PdCu nanoparticles and commercial Pd/C in 0.1 M KOH electrolyte. Particularly, PdCu nanotubes show Pt-like performance, and achieve an onset potential of 0.941 V (vs. RHE) and a half potential of 0.825 V. The electron transfer number during oxygen reduction is close to 4 on PdCu nanotubes. Moreover, the catalytic stability of the obtained one-dimensional PdCu nanocrystals is much superior to that of commercial Pd/C and PVC catalysts.