Modern tissue engineering aims to create materials which promote, possibly in a controlled way, cell adhesion. These artificial three-dimensional structures should be capable of promoting the cell growth and gradually be replaced by new tissue. They cannot be considered as a standing substitute of a tissue, but as a temporary structure which promotes regeneration. Here, a biodegradable DegraPol® (DP), a polyester urethane, was used as a matrix which mechanical, electrical and cell adhesion properties ought to be modified by addition of graphene oxide (GO). Using solution electrospinning method four samples containing different quantities of GO (0, 0.5, 1.0, 2.0 wt%) were obtained. In order to produce fibrous scaffolds with increased porosity, solutions of DP and GO were co-spun with a water soluble polymer, polyethylene oxide (PEO), which was subsequently removed. Morphological and mechanical properties of the scaffolds were studied. Proper fiber formation was possible in the range of 8–14 wt% DP in a mixture of chloroform and ethanol in a ratio of 80:20 (wt/wt). The best homogeneity of the fibers was achieved for 12 wt% DP. The addition of GO had not changed much the morphology of the fibers. The co-electrospining of the polymers was successfully performed resulting in a mesh formation consisted of both polymers. The tensile test showed that the presence of GO in the DP matrix first increased the tensile strength, reaching the maximum value of 7.15 MPa, and then for higher GO content it started to decrease. Elongation at break (EB) had the highest value for the unfilled DP of 511 % and then it decreased with addition of GO and increase of its content. After removal of PEO from co-electrospun scaffolds, the values of the mechanical properties, TS and EB, of these porous samples significantly drop.