In this study, we have used a seed-mediated growth approach to prepared monodispersive Au–Pd core–shell heterostructures by pre-synthesized 50 nm Au octahedral nanocrystals developed previously. Systematical shape evolution from cubic to truncated cubic, cuboctahedral, truncated octahedral and octahedral structures are achieved by changing the volumes of Au nanooctahedra solutions 0.45 mL to 0.40 mL, 0.35 mL, 0.30 mL and 0.2 mL per 10 ml total volume of reaction mixture. The cetyltrimethylammonium bromide (CTAB) we used, is not only served as capping agent but also changing reduction rate to perform shape controlled synthesis of Au–Pd core–shell heterostructures. CTAB can react with PdCl42– and convert it into the complex–surfactant aggregates [CTA]2[PdBr4]. Transmission electron microscopy (TEM), Powder X-ray diffraction (PXRD) and scanning electron microscopy (SEM) have been applied to characterize the surface of crystalline facets. High index facets of unusual concave cubic structure were characterized by high resolution transmission electron microscopy (HR–TEM) and transmission electron microscopy. We can determine Miller indexes of these High index facets by measuring the angle between facets of the projected concave nanocube and {100} face of an ideal cube. Time-dependent UV–vis absorption spectra were used for monitoring the reactions and demonstrating the growth mechanism. It shows that a slow reduction rate of the palladium source for promoting the formation of {111} shell which is manipulated by the amount of the Au cores used. Suzuki–Miyaura coupling reaction were used for comparing the catalytic activity of concave cubic and octahedral Au–Pd core–shell heterostructures. The concave cubic structures give better performance by half reaction time of octahedra structures. However, both of them show the good recyclability in the catalytic reaction.