The increased demand for vascular grafts for the treatment of cardiovascular diseases has led to the search for novel biomaterials that can achieve the properties of the tissue. According to this, the investigation of polyurethanes has been a promising approach to overcome the present limitations. However, some biological properties remain to be overcome, such as thrombogenicity and hemocompatibility, among others. This paper aims to synthesize polyurethanes based on castor oil and castor oil transesterified with triethanolamine (TEA) and pentaerythritol (PE) and with the incorporation of 1% chitosan. Analysis of the wettability, enzymatic degradation, mechanical properties (tensile strength and elongation at break), and thermal stability was performed. Along with the evaluation of the cytotoxicity against mouse fibroblast (L929) and human dermal fibroblast (HDFa) cells, the hemolysis rate and platelet adhesion were determined. The castor-oil-based polyurethanes with and without 1% chitosan posed hydrophobic surfaces and water absorptions of less than 2% and enzymatic degradation below 0.5%. Also, they were thermally stable until 300 °C, with tensile strength like cardiovascular tissues. The synthesized castor oil/chitosan polyurethanes are non-cytotoxic (cell viabilities above 80%) to L929 and HDFa cells and non-thrombogenic and non-hemolytic (less than 2%); therefore, they are suitable for cardiovascular applications.