We report the first measurement of the charm-mixing parameter y(CP) in D-0 decays to the CP-odd final state K-S(0 omega). The study uses the full Belle e(+)e(-) annihilation data sample of 976 fb(-1) taken at or near the gamma (4S) centre-of-mass energy. We find y(CP) = (0.96 +/- 0.91 +/- 0.62(-0.00)+0.17)%, where the first uncertainty is statistical, the second is systematic due to event selection and background, and the last is due to possible presence of CP-even decays in the data sample.