The high Curie temperatures and compatible lattice structure with conventional semiconductors for half-metallic Co₂FeZ and Co₂CrZ (Z=Al, Si, Ga, Ge) inspired us to design new quaternary Heusler half-metallic ferromagnets CoFeCrZ. Our first-principles calculations show that, within generalized gradient approximation for the electronic exchange–correlation functional, both CoFeCrGa and CoFeCrGe are nearly half-metals, while both CoFeCrAl and CoFeCrSi exhibit excellent half-metallic ferromagnetism with the large half-metallic gaps of 0.16 and 0.28eV, respectively. The half-metallicity of CoFeCrAl and CoFeCrSi is robust against the lattice compression (up to 7% and 4%, respectively). We also reveal that the half-metallicity is lost for both CoFeCrAl and CoFeCrGa but retentive for both CoFeCrSi and CoFeCrGe when the Coulomb interactions are considered. In addition, both CoFe- and CrSi-terminated (001) surfaces with and without antisite defects lose the bulk half-metallicity in CoFeCrSi.