A proton-proton collision data sample, corresponding to an integrated luminosity of 3 fb(-1) collected by LHCb at root s = 7 and 8 TeV, is used to reconstruct 63 +/- 9 Omega(-)(b) -> Omega(0)(c)pi(-), Omega(0)(c) -> pK(-)K(-)pi(+) decays. Using the Xi(-)(b) ->Xi(0)(c)pi(-), Xi(0)(c) -> pK(-)K(-)pi(+) decay mode for calibration, the lifetime ratio and the absolute lifetime of the Omega(-)(b) baryon are measured to be tau(Omega b-)/tau(Xi b-) = 1.11 +/- 0.16 +/- 0.03, tau(Omega b-) = 1.78 +/- 0.26 +/- 0.05 +/- 0.06 ps, where the uncertainties are statistical, systematic and from the calibration mode (for tau(Omega b-) only). A measurement is also made of the mass difference, m(Omega b-) - m(Xi b-), and the corresponding Omega(-)(b) mass, which yields m(Omega b-) - m(Xi b-) = 247.4 +/- 3.2 +/- 0.5 MeV/c(2), m(Omega b-) = 6045.1 +/- 3.2 +/- 0.5 +/- 0.6 MeV/c(2). These results are consistent with previous measurements.