Abstract: A Compton backscattering X-ray source, which is based on a superconducting accelerator and energy recovery linac (ERL), driven by the DC-SC photocathode injector developed at Peking University, was proposed and preliminarily designed. Analytical calculations and simulations show that the X-ray source has very promising characteristics, which may provide quasi-monochromatic X-ray photons with very high flux.