We report de Haas-van Alphen (dHvA) effect measurement of the intermediate-valence compound CeCoSi3 whose crystal structure lacks space-inversion symmetry. Some dHvA frequencies of CeCoSi3 qualitatively correspond to those of CeRhSi3 which is a heavy-fermion antiferromagnet exhibiting pressure-induced superconductivity. We observed multiply splitting dHvA frequencies and attributed them to the magnetic breakdown between two separated Fermi surfaces due to the antisymmetric spin-orbit coupling (ASOC). Strikingly, the cyclotron effective masses of the separated Fermi surfaces are largely different, indicating that the mass enhancement depends on the spin direction. The evaluated ASOC energy of CeCoSi3 is less than that of LaCoGe3, which is probably characteristic of a heavy-fermion band with an itinerant f-electron.