The　difference　between　the　actual　feeder　parameters　and　feeder　parameter　data　stored　in　a　database　or　offered　by　manufacturers　is　significant　owing　to　the　ambient　environment,　temperature,　and　skin　effect.　Here,　a　parameter　estimation　method　is　proposed　for　unbalanced　three-phase　distribution　feeders　based　on　the　bus　voltages　and　branch　power　flows　measured　from　two　terminals　of　the　feeder.　In　the　proposed　method,　a　high-precision　phasor　measurement　unit　is　not　required　to　estimate　the　magnitude　and　phase　angle　of　the　phasor　quantity　using　a　common　time　source　for　synchronisation.　A　radial　basis　function　neural　network　with　multi-run　optimisation　(RBFNN-MRO)　is　proposed　to　map　the　complex　nonlinear　relations　between　the　distribution　feeder　parameters　and　electrical　quantities.　The　feasibility　and　performance　of　the　proposed　RBFNN-MRO　method　were　verified　using　the　four　IEEE　test　systems.　The　comparison　between　the　proposed　RBFNN-MRO　method　and　the　multi-run　method　based　on　the　quasi-Newton　method　is　implemented　via　the　maximum　absolute　percentage　error　(MAPE)　curves.　The　results　reveal　that　the　proposed　RBFNN-MRO　method　has　excellent　potential　for　improving　the　accuracy　of　feeder　parameter　estimation,　even　for　bad　data　preparation.