BasedontheDyson-Schwingerequationsofquarkpropagatorinrainbowtruncationwithaneffectivegluonpropagator,thetenunknownGasser-LeutwylercoefficientsofthechiralLagrangianforpseudoscalarGoldstonebosonsarepredicted.ThepredictedvaluesofL_iwithi=1,2,...,10areinareasonableagreementwithempiricalvaluesusedwidelyinliterature,andthevaluespredictedbymanyothertheoreticalmodelswithQCDcharacteristics.