We have performed a sub-meV photoemission study on Mg(B1-xCx)(2) for x = 0-0.075. The superconducting (SC) transition temperature (T-c) changes systematically from 38 K to 24 K with increasing the carbon concentration. Because of the extremely high-energy resolution of sub-meV, two features corresponding to the two SC gaps originated from pi and sigma bands are clearly observed even in raw spectra up to x = 0.075. From numerical analyses, we found that the gap size of the sigma band is proportional to T-c, while that of the pi band is almost constant. The temperature and carbon concentration dependences of the two gaps are explained within a simple two-band model based on a mean field theory. Using the theoretical model, we deduced interband and intraband coupling strength constants. The transition temperature is dominated by the intraband coupling of the sigma band, while the interband coupling slightly increases with increasing the carbon concentration. The two-band model shows that the interband coupling slightly pushes up T-c. (c) 2007 Elsevier B.V. All rights reserved.