We report on measurements of the mass and lifetime of the Xi(-)(b) baryon using about 1800 Xi(-)(b) decays reconstructed in a proton-proton collision data set corresponding to an integrated luminosity of 3.0 fb(-1) collected by the LHCb experiment. The decays are reconstructed in the Xi(-)(b) -> Xi(0)(c)pi(-), Xi(0)(c) -> pK(-)K(-)pi(+) channel and the mass and lifetime are measured using the Lambda(0)(b) -> Lambda(+)(c)pi(-) mode as a reference. We measure M(Xi(-)(b)) - M(Lambda(0)(b)) = 178.36 +/- 0.46 +/- 0.16 MeV/c(2), (tau Xi(-)(b)/tau Lambda(0)(b)) = 1.089 +/- 0.026 +/- 0.011, where the uncertainties are statistical and systematic, respectively. These results lead to a factor of 2 better precision on the Xi(-)(b) mass and lifetime compared to previous best measurements, and are consistent with theoretical expectations.