In order to explain the experimental results of resistivity minima in Au1-xNix alloys (x=0.30-0.42) at low temperature, we propose a model of the alloy with dilute spin clusters in the paramagnetic state based on the s-d interaction. The resistivity contribution from the electron scattering by isolate spin clusters and by spin clusters with a ferromagnetic RKKY interaction are considered. Combining with the phonon contribution, derived from the experimental data of ρi(T) of Au-Cu or Au80Ni20 alloy, we obtain a resistivity minimum. The calculated total resistivity ρ(T) is in good agreement with the experimental result. It is shown that a decrease in ρ with increasing temperature below Tmin is mainly attributed to the Kondo effect caused by isolate spin clusters. The electron scattering from coupled spin cluster pairs gives a much smaller contribution to the resistivity, which exhibits a T-1 temperature-dependence and decreases rapidly with increasing temperature. So the experimental relults of ρ(T)-ρi(T) in Au1-xNix alloys (x=0.30-0.42) show a log T temperature-dependence over a wide tempera-ture range.