Abstract : The production fractions of charged and neutral b-hadrons in b-quark events from Z0 decays have been measured with the DELPHI detector at LEP. An algorithm has been developed, based on a neural network, to estimate the charge of the weakly-decaying b-hadron by distinguishing its decay products from particles produced at the primary vertex. From the data taken in the years 1994 and 1995, the fraction of bbar-quarks fragmenting into positively charged weakly-decaying b-hadrons has been measured to be: f^+ = (42.09 +/- 0.82 (stat.) +/- 0.89 (syst.))%. Subtracting the rates for charged Xibar_b^+ and Omegabar_b^+ baryons gives the production fraction of B^+ mesons: f_Bu = (40.99 +/- 0.82 (stat.) +/- 1.11 (syst.))%.