The prompt production of +c baryons is studied in proton- lead collisions collected with the LHCb detector at the LHC. The data sample corresponds to an integrated luminosity of 1 : 58 nb recorded at a nucleon- nucleon centre- of- mass energy of p sNN = 5 : 02TeV. Measurements of the di ff erential cross- section and the forwardbackward production ratio are reported for +c baryons with transverse momenta in the range 2 < pT < 10 GeV =c and rapidities in the ranges 1 : 5 < y < 4 : 0 and 4 : 5 < y < 2 : 5 in the nucleon- nucleon centre- of- mass system. The ratio of cross- sections of +c baryons and D0 mesons is also reported. The results are compared with next- to- leading order calculations that use nuclear parton distribution functions.