Abstract: In tbe paper,the fan model from Australia is adopted as a quantitative model of apatite fission-track annealing. The authors modelled the length distribution of apatite fission-tracks along certain temperature-time paths on the basis of fission-track annealing atvariable temperatures using the equivalent time principle;the length distribution of a series of fossion-tracks produced at a sufficient short time being approached by a Qatiss den-sity function;and the superimposed length distributions of fission-tracks prodticed successively throughrout geohistory.Some qualitatively discriminant models,herein for theanalysis of geothermal history of sedimentary basins,are presented by numerical modellings on the distributions of apatite fission-tracks along several geothermal temperaturepaths and their correlations. It is proposed that a further modelling on the geohistory andgeothermal history sedimentary basins can be achieved with such a discriminant model andfinanlly,the numerical modelling is applied for the thermal history and stratigraphic de-nudation of Qiou No.3 well.