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The application of appropriate constitutive equation describing the relationship between the flow stress, temperature and strain rate is essential to get deep insight into the process mechanism of friction stir welding (FSW). The phase-field simulation of dynamic recrystallization (DRX) suitable for FSW process is specifically integrated into the modification of the constitutive relationship. The variation of dislocation density and stress with strain rate and temperature are quantitatively analyzed. The DRX softening coefficient varying with temperature and strain rate is proposed to express the DRX softening effect on the flow stress. The modified constitutive equation considering the DRX softening effect is applied in the FSW process model to calculate the flow stress, temperature, strain rate, velocity magnitude and material flow streamlines, and the prediction accuracy is improved.