The goal of this work is to fabricate a new composite based on polyurethane (PU), grapefruit (GP) oil, and cobalt nitrate [Co(NO3)2] using an electrospinning technique. Morphology results revealed the reduction in the fiber diameter of the composites compared to pristine PU control. The interaction of PU with GP and Co(NO3)2 was confirmed by hydrogen bond formation evident in infrared analysis. The fabricated PU/GP composites depicted a more hydrophobic behavior, while PU/GP/Co(NO3)2 showed a hydrophilic behavior than the pristine PU. Atomic force micrographs (AFM) revealed that the developed composites showed a decrease in the surface roughness (Ra) compared to PU. The addition of GP and Co(NO3)2 improved the mechanical strength of the pristine PU. The blood compatibility assays concluded not only the increase in blood clotting levels but also the less toxic nature of the fabricated composites compared to the pristine PU. Hence, the newly designed composites possessing outstanding physicochemical and biological properties may be used as a potential candidate for scaffolding in tissue engineering applications.