The chemical fixation of CO2 with a more effective pathway is of great significance from the sustainable chemistry viewpoint. Herein, a novel fiber-supported superbase was successfully synthesized by rooting 1,5,7-triazabicyclo[4.4.0]dec-5-ene (TBD) into the surface layer of commercially available polyetheretherketone (PEEK) fiber and efficiently served as a heterogeneous catalyst for the conversion of CO2 in a sample spinning basket reactor. The resulting fiber samples were characterized detailedly by elemental analysis, mechanical property, FTIR spectroscopy and morphology during both of the preparation and the utilization processes. Moreover, the fiber catalyst was applied in the spinning basket reactor under mild conditions (100 °C and 1 MPa) for the cycloaddition of CO2 with a series of 2-aminobenzonitriles in water to obtain good to excellent yields of the corresponding quinazoline-2,4-(1H,3H)-diones (82–95%). In addition, the fiber-supported TBD in impellers of the agitation system was shown to be reused over 15 times without distinctly performance degradation, and stored on shelves remained equally active after at least up to 4 months. Furthermore, the operation process was convenient and effective for scaling-up procedure and thereby the fiber catalyst has good prospects in industrial applications.