Anodic aluminium oxide (AAO) is a self-organised nanopore that has been widely studied due to the ease of its synthesization and pore properties manipulation. However, pore growth behaviour under different geometrical surfaces is rarely studied, particularly on the effect of combined curved surfaces towards pore growth properties, which is crucial in designing unique porous platform for specific applications. This paper reports study on the decisive effect of curvature surfaces on development of pore structure and properties at a constant potential. In this work, AAO grown on treated convex and concave surfaces were analysed in terms of pore quantity, pore diameter, interpore distance, pore length and other parameters of pore bottom geometry in conjugation with observation of pore cessation, bifurcation, bending and tapering. The unique formation of tapered pore was observed and described. Major factors deciding pore properties under curved surfaces were identified and discussed. We introduced a new parameter for surface quantification known as central inscribed angle, which was identified to be the central factor which decides pore growth behaviour under a curvature. Here, we observed a different trend in growth rate of pores under different curvatures, which oppose the commonly accepted convex > planar > concave pattern. Levelling height was later identified to be the decisive factor in determining growth rate of pores under a curvature at different geometrical location. These findings open up possibility to precisely control and tailor the growing path and pore structures of AAO simply via anodising an Al sheet under combined curvature surfaces, which could be beneficial for future novel applications.