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The effect of doping on the half-metallicity and magnetism of Co2-xCrxCrAl (x=0-1) alloys was studied by full-potential linearized-augmented plane wave (FLAPW) calculations. With increasing Cr content, a transition from the half-metallic ferromagnet (HMF) to the half-metallic completely compensated ferrimagnet (HMCCF, also called half-metallic antiferromagnet) is observed. The calculations indicate that Co2-xCrxCrAl alloys are half-metallic within the whole range studied. Substitution of Cr for Co leads to a large antibonding peak above EF in the majority-spin band, but still keeps the energy gap in the minority-spin band. The size of the gap is mainly determined by the density of states (DOS) of atoms at the (A, C) sites. With increasing Cr content, the total spin moment decreases linearly from 3muB/f.u. to zero, which obeys the Slater-Pauling curve quite well. The spin moment of Cr at the C site is antiferromagnetically aligned with the magnetic moments of the Cr (B) and the Co atoms. This antiferromagnetic coupling causes a monotonic decrease of the total magnetic moment.