This study proposes a ID model that describes the time variations of the spreading ratio for a non-Newtonian (shear-thinning) liquid drop impinging on dry solid surfaces. This model is based on the previous model developed for Newtonian liquids, where an energy balance approach with a cylindrical disk approximation was adopted and the dissipation mechanism near the contact line was taken into account. The present model showed good predictions for the spreading behavior, and accordingly the maximum spreading ratios were predicted with 97% of the data within +/- 10% accuracy. Also, the model predictions of the receding behavior for a low-viscosity drop impinging on a hydrophobic surface were in good agreement with the experiments. However, the discrepancy in the receding behavior became larger for the higher-viscosity drop impacting on a hydrophilic surface because the contact angle hysteresis appears more prominent. Based on this model, the time variations of the liquid viscosity for an impinging shear-thinning drop were simulated, and the effects of non-Newtonian liquid rheological parameters in the Cross model on the postimpingement behavior were also examined in detail. Consequently, it was found that the liquid viscosity in a high shear rate range dominates the spreading and receding behavior of a shear-thinning drop.