The lifetimes of charged and neutral B hadrons have been measured using data collected by the DELPHI experiment at LEP between 1991 and 1993. B hadrons are tagged as jets with a secondary vertex and the charge of the B candidate is taken to be the sum of the charges of the particles in the secondary vertex. Approximately 1,434,000 multihadronic Z0 decays yielded 1817 B hadron candidates. The B purity was estimated to be around 99.1±0.3%, and 83% (70%) of the events measured as neutral (charged) came from neutral (charged) B's. The mean lifetimes of charged and neutral B hadrons were found to be 1.72±0.08 (stat.) ±0.06 (syst.) ps and 1.58±0.11 (stat.)±0.09 (syst.) ps respectively. The ratio of their lifertimes, tcharged/tneutral, was 1.09-0.10+0.11 (stat.)±0.08 (syst.). By making assumptions about the Bs0 and ?b0 states, the B+ and B0 meson lifetimes were determined to be tB+ = 1.72 ± 0.08 (stat.) ±0.06 (syst.) ps and tB+ = 1.63 ± 0.14 (stat.)±0.13 (syst.) ps and the ratio of their lifetimes was.