The Bayesian neural network (BNN) method is proposed to predict the isotopic cross-sections in proton induced spallation reactions. Learning from more than 4000 data sets of isotopic cross-sections from 19 experimental measurements and 5 theoretical predictions with the SPACS parametrization, in which the mass of the spallation system ranges from 36 to 238, and the incident energy from 200 MeV/u to 1500 MeV/u, it is demonstrated that the BNN method can provide good predictions of the residue fragment cross-sections in spallation reactions.