A novel high precision method measures the b-quark forward-backward asymmetry at the Z pole on a sample of 3,560,890 hadronic events collected with the DELPHI detector in 1992 to 2000. An enhanced impact parameter tag provides a high purity b sample. For event hemispheres with a reconstructed secondary vertex the charge of the corresponding quark or anti-quark is determined using a neural network which combines in an optimal way the full available charge information from the vertex charge, the jet charge and from identified leptons and hadrons. The probability of correctly identifying b-quarks and anti-quarks is measured on the data themselves comparing the rates of double hemisphere tagged like-sign and unlike-sign events. The b-quark forward-backward asymmetry is determined from the differential asymmetry, taking small corrections due to hemisphere correlations and background contributions into account. The results for different centre-of-mass energies are: Ab FB (89.449 GeV) = 0.0637 ± 0.0143(stat.) ± 0.0017(syst.) , Ab FB (91.231 GeV) = 0.0958 ± 0.0032(stat.) ± 0.0014(syst.) , Ab FB (92.990 GeV) = 0.1041 ± 0.0115(stat.) ± 0.0024(syst.) . Combining these results yields the b-quark pole asymmetry Ab,0 FB = 0.0972 ± 0.0030(stat.) ± 0.0014(syst.)