In this work, bioinspired anisotropic polymeric heart valves were fabricated using composite materials from polyurethane (PU) and natural cellulose fiber bundles. Cellulose fibers with good alignment were obtained from balsa wood by a top-down process, which were then distributed in polyurethane to prepare cellulose fiber bundles reinforced polyurethane (CPU) by hot pressing. The storage modulus of the CPU along the direction parallel to the fiber alignment was 16.70 ± 0.80 MPa, whereas that along the direction perpendicular to the fiber alignment was 8.41 ± 0.94 MPa by dynamic mechanical analysis (DMA) tests at 1 Hz, comparable to aortic valve leaflets. Moreover, 2-methacryloyloxyethyl phosphorylcholine (MPC) was grafted onto the CPU surface (CPU-MPC) to improve hemocompatibility. With MPC modification, the water contact angle decreased significantly from 54.58° ± 2.98° to 26.42° ± 3.50°, and the platelet adhesion was reduced by 92%, compared to the original CPU. In vitro cell culture proved that both CPU and CPU-MPC samples did not show any cytotoxicity. Furthermore, the CPU composites were used to fabricate polymeric heart valves, which showed excellent hydrodynamic performance with a large orifice area (1.70 cm2) and low regurgitation fraction (0.7%), meeting the requirements of ISO 5840-2 standard.