Agricultural tractors drive and operate both off-road and on-road. Tire–road interaction significantly affects the tractive performance of a tractor, which is difficult to predict numerically. Many empirical models have been developed to predict the tractive performance of tractors using the cone index, which can be measured through simple tests. However, a magic formula model that can determine the tractive performance without a cone index can be used instead of traditional empirical models as the cone index cannot be measured on asphalt roads. The aim of this study was to predict the tractive performance of a tractor using the magic formula tire model. The traction force of the tires on an asphalt road was measured using an agricultural tractor. The dynamic wheel load was calculated to derive the coefficients of the traction–slip curve using the measured static wheel load and drawbar pull of the tractor. Curve fitting was performed to fit the experimental data using the magic formula. The parameters of the magic formula tire model were well identified, and the model successfully determined the coefficient of traction of the tractor.