To enhance the angular stability of Frequency Selective Surface (FSS) absorbers, a broadband absorber is designed by using an Indium Tin Oxide (ITO) resistive film in combination with a dielectric compensation layer. This absorber features flexibility, transparency, polarization insensitivity, and high angular stability. The 90% absorption bandwidth of the absorber covers the frequency range of 5.66 to 22.98 GHz, achieving a relative bandwidth of 121.0%. When the incidence angle of the electromagnetic wave varies from 0° to 60°, the absorber maintains an absorption rate of over 80% in the frequency band of 7.00 to 22.86 GHz. Fabrication and experimental testing have shown that the designed FSS absorber exhibits good transparency and flexibility, with test results matching well with simulation results, thereby validating the rationality of the design. Moreover, when the sheet resistance of the resistive film and the relative permittivity of the dielectric layer fluctuate within certain ranges due to manufacturing processes, the absorber structure can still achieve broadband absorption and maintain high angular stability. This significantly enhances the engineering practicability of the designed absorber in applications such as stealth and electromagnetic interference suppression for the windows and doors of aircraft and vehicles.