We investigated the Ge-composition (γ) dependence of the saturation magnetization of CFGG thin films and the magnetoresistance (MR) ratio of CFGG-based current-perpendicular-to-plane giant magnetoresistance (CPP-GMR) devices together with first-principles calculations of the electronic states of CFGG. Theoretical calculations showed that spin polarization is highest at the stoichiometric composition γ = 0.56 in Co2Fe1.03Ga0.41Ge
γ
and that it decreases in off-stoichiometric CFGG, mainly due to the formation of CoFe antisites for Ge-deficient compositions and FeCo antisites for Ge-rich compositions, where CoFe (FeCo) indicates that Co (Fe) atoms replace the Fe (Co) sites. The saturation magnetic moment (μs
) per formula unit decreased monotonically as γ increased from 0.24 to 1.54 in Co2Fe1.03Ga0.41Ge
γ
. The μs
was closest to the Slater-Pauling value predicted for half-metallic CFGG at the stoichiometric composition γ = 0.56, indicating that stoichiometric CFGG has a half-metallic nature. This is consistent with the result for the theoretical spin polarization. In contrast, the MR ratio of CFGG-based CPP-GMR devices increased monotonically as γ increased from 0.24 to 1.10, and reached a huge MR ratio of 87.9% at the Ge-rich composition γ = 1.10. Then, the MR ratio decreased rapidly as γ increased from 1.10 to 1.48. Possible origins for the slight difference between the Ge composition at which the highest MR ratio was obtained (γ = 1.10) and that at which the highest spin polarization was obtained (γ = 0.56) are improved atomic arrangements in a Ge-rich CFGG film and the reduction of effective Ge composition due to Ge diffusion in the GMR stacks.