Poly(3-hydroxybutyrate) (P3HB) is a biopolymer, but storing products from P3HB causes the deterioration of their properties leading to their brittleness. P3HB has also low thermal stability. Its melting point almost equals its degradation temperature. To obtain biodegradable and biocompatible materials characterized by higher thermal stability and better strength parameters than the unfilled P3HB, composites with the addition of polyurethanes were produced. The morphology, thermal, and mechanical property parameters of the biocomposites were examined using scanning electron microscopy, thermogravimetric analysis, standard differential scanning calorimetry, and typical strength machines. Aliphatic polyurethanes, obtained by the reaction of 1,6-hexamethylene diisocyanate and polyethylene glycols, were used as modifiers. To check the influence of the glycol molar mass on the properties of the biocomposites, glycols with a molecular weight of 400 and 1000 g/mol were used. New biocomposites based on P3HB were produced with 5, 10, 15, and 20 wt. % content of polyurethane by direct mixing using a twin-screw extruder. The following property parameters of the prepared biocomposites were tested: degradation temperature, glass transition temperature, tensile strength, impact strength, and Brinell hardness. Improvement of the processing property parameters of P3HB-biocomposites with the addition of aliphatic polyurethanes was achieved by increasing the degradation temperature in relation to the degradation temperature of the unfilled P3HB by over 30 °C. The performance property parameters have also been improved by reducing the brittleness compared to the P3HB, as evidenced by the increase in impact strength and the decrease in hardness with an increase in the amount of polyurethane obtained by the reaction of 1,6-hexamethylene diisocyanate and polyethylene glycol with a molecular weight of 400 g/mol (PU400) as modifier.