The promotion of angiogenesis is a fundamental step for efficient organ/tissue reconstitution and replacement. Thus, several strategies to promote vascularization of scaffolds were studied to satisfy this unsolved clinical need. The interface between cells and substrates is a determinant for the success of tissue engineering (TE) strategies. Substrate's topography is reported to play a key role in influencing endothelial cell behavior, namely, on its proliferation, metabolic activity, morphology, migration, and secretion of cytokines and chemokines. Therefore, surface topography of the biomaterial-based grafts is a crucial property that is considered in the development of a new TE approach. Herein, we hypothesize that the surface of Rubus fruticosus leaf plays a crucial role in driving angiogenesis since its architecture resembles the vascular structures at a biologically relevant size scale. For this, we produced biomimetic polycaprolactone (PCL) membranes (BpMs) replicating the surface topography of a R. fruticosus leaf by replica molding and nanoimprint lithography. Our results showed an enhanced performance in terms of proliferation of the human endothelial cell line on top of the BpM. Moreover, an asymmetric cellular spatial distribution among the surface of the BpM was observed. These cells seem to have higher density for longer time periods in the region that replicates the leaf veins. Finally, we assess the angiogenic capacity through a chick chorioallantoic membrane assay, revealing that BpMs are more prone to support angiogenesis than flat PCL membranes. We strongly believe that this strategy can bring new insights into developing TE strategies with an enhanced performance in terms of the vascular integration between the host and the scaffolds implanted.