Tissue engineering is based on the association of cultured cells with structural matrices and the incorporation of signaling molecules for inducing tissue regeneration. Despite its enormous potential, tissue engineering faces a major challenge concerning the maintenance of cell viability after the implantation of the constructs. The lack of a functional vasculature within the implant compromises the delivery of nutrients to and removal of metabolites from the cells, which can lead to implant failure. In this sense, our investigation aims to develop a new strategy for enhancing vascularization in tissue engineering constructs. This study's aim was to establish a culture of human adipose tissue-derived stem cells (hASCs) to evaluate the biocompatibility of electrospun fiber mesh made of polyhydroxybutyrate (PHB) and its copolymer poly-3-hydroxybutyrate-co-3-hydroxyvalerate (PHB-HV) and to promote the differentiation of hASCs into the endothelial lineage. Fiber mesh was produced by blending 30% PHB with 70% PHB-HV and its physical characterization was conducted using scanning electron microscopy analysis (SEM). Using electrospinning, fiber mesh was obtained with diameters ranging 300 nm to 1.3 µm. To assess the biological performance, hASCs were extracted, cultured, characterized by flow cytometry, expanded and seeded onto electrospun PHB/PHB-HV fiber mesh. Various aspects of the cells were analyzed in vitro using SEM, MTT assay and Calcein-AM staining. The in vitro evaluation demonstrated good adhesion and a normal morphology of the hASCs. After 7, 14 and 21 days of seeding hASCs onto electrospun PHB/PHB-HV fiber mesh, the cells remained viable and proliferative. Moreover, when cultured with endothelial differentiation medium (i.e., medium containing VEGF and bFGF), the hASCs expressed endothelial markers such as VE-Cadherin and the vWF factor. Therefore, the electrospun PHB/PHB-HV fiber mesh appears to be a suitable material that can be used in combination with endothelial-differentiated cells to improve vascularization in engineered bone tissues.