Creating scaffolds for skin tissue engineering remain challenging in terms of their mechanical and biological properties. In this paper, we present a study on the nanocomposite polyurethane (PU)/polycaprolactone (PCL) scaffolds with graphene oxide (GO), which were fabricated by using electrospinning method, for potential skin tissue engineering. For this, homogenous and soft PU nanofibers containing varying percent of polycaprolactone (12% and 15%) and nano GO (0.5-4%) were electrospun, respectively, and then characterized by different techniques/assays in vitro. For the scaffold characterization, scanning electron microscopy (SEM) and Fourier-transform infrared spectroscopy (FTIR) were used. The SEM results show the spun scaffolds have 3D porous structure (90%) with the fiber diameter increased with the GO concentration, while the FTIR results confirmed the presence of PU, PCL, and Go in the scaffolds. Also, the biocompatibility, via the cytotoxicity, of the scaffolds was examined by MTT assay with the human skin fibroblast cells, along with their wettability in terms of contact angle. Our results show that the scaffolds are biocompatible to the skin fibroblast cell, illustrating their potential use in skin tissue engineering. Also, our results illustrate that the addition of GO to the PU/PCL composite can increase the wettability (or hydrophilicity) and biocompatibility of scaffolds. Combined together, the nanocomposite PU/PCL scaffolds with GO are promising as biocompatible constructs for skin tissue engineering.