Abstract: In this work, the gas-Cherenkov detector with an off-axis parabolic reflector (OprGCD) is designed using the Geant4 Monte Carlo simulation toolkit, which is helpful to improve the collection efficiency of Cherenkov photons. The method to study the performance of OprGCD based on femtosecond laser-wakefield-accelerated electron beams is presented. Cherenkov signals with high signal-to-noise ratio were obtained, and the measured Cherenkov signals changing with the CO₂ pressure were consistent well with the simulation results. The design and study of this OprGCD system lay the foundation for the application of fusion gamma diagnostics system in large laser facilities of China.