A precision measurement of the B-c(+) meson mass is performed using proton- proton collision data collected with the LHCb experiment at centre-of-mass energies of 7, 8 and 13 TeV, corresponding to a total integrated luminosity of 9.0 fb(-1). The B-c(+) mesons are reconstructed via the decays B-c(+)-> J/psi pi(+), B-c(+)-> J/psi pi(+)pi(-)pi(+), B-c(+)-> J/psi pppi(+), B-c(+)-> J/psi D-s(+), B-c(+)-> J/psi (DK+)-K-0 and B-c(+)-> B-s(0)pi(+). Combining the results of the individual decay channels, the B-c(+) mass is measured to be 6274.47 +/- 0.27 (stat) +/- 0.17 (syst) MeV/c(2). This is the most precise measurement of the B-c(+) mass to date. The difference between the B-c(+) and B-s(0) meson masses is measured to be 907.75 +/- 0.37 (stat) +/- 0.27 (syst) MeV/c(2).