Enhancing the biocompatibility profiles including cell attachment, growth, and viability and mechanical properties of designed synthetic scaffolds have an essential role in tissue engineering applications. Polymer blending is one of the most effective methods for providing new anticipated biomaterials for tissue scaffolds. Here, the blend solution of the different mass weight ratio of polycaprolactone (PCL) to human serum albumin (HSA) was subjected to fabricate nanocomposite spider-web-like membranes using electrospinning process. The physicochemical aspects of fabricated membranes had been characterized by a different state of techniques like that of scanning electron microscopy (FE-SEM), Fourier transform infrared spectroscopy (FT-IR), thermal gravimetric analysis (TGA), contact angle meter and universal testing machine. FE-SEM images revealed that all PCL/HSA mats were composed of interlinked nano-nets along with conventional electrospun fibers while nano-nets were not found for pristine PCL mat. Moreover, composite membranes exhibited improved water absorbability, enhanced biodegradation compared to pristine PCL membrane and had much better mechanical properties (tensile strength increased by up to 3-fold, Young's modulus by 2-fold). The cell attachment and proliferation tests were carried by culturing Mc3T3-E1 (pre-osteoblasts) with the designated nanofibrous membranes. The hybrid nanofibers exhibited extraordinary support for the adhesion and proliferation of cells when compared to the pristine PCL membrane. These results indicate that the nano-nets supported PCL/HSA scaffolds can be promising for tissue engineering applications.