A new quaternary fluoroarsenide CaFeAsF with the tetragonal ZrCuSiAs-type structure composed of alternate stacking of (FeAs)(delta-) and (CaF)(delta+) layers was synthesized. CaFeAsF is a poor metal and shows the anomaly at similar to 120 K in temperature dependence of electrical conductivity. The electron doping by the partial replacement of the iron with cobalt suppresses the anomaly and induces the bulk superconductivity (optimal T-c = 22 K for CaFe0.9Co0.1AsF), analogues to recently discovered FeAs-based superconductors. The present results suggest that CaFeAsF is a promising candidate as a parent compound for high T-c superconductors.