"Sub-meV" resolution photoemission spectroscopy was used to study carbon-substitution dependence of the multiple superconducting gap of Mg (B1-x Cx) 2. Two features corresponding to σ and π gaps are clearly observed in the raw spectra up to carbon concentration x=0.075. The observed x dependence of the two gaps shows a qualitatively different behavior: the σ gap is proportional to Tc while the π gap shows negligible change. Doping as well as temperature dependence can be explained within the two-band mean-field theory. Implications from the present study are discussed. © 2005 The American Physical Society.