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Continuous models for the prediction of the grain growth and recrystallization kinetics can be roughly classified into two methods. One method is multi-phase-field approaches. The second method is the phase-field model of Kobayashi, Warren and Carter (KWC) with two or three order parameters that make the model more efficient and more promising for the description of polycrystals. The present work proposes an extension to the KWC model to incorporate the recrystallization process by means of an additional order parameter for recrystallized grains. The results of the simulation of the grain growth and recrystallization process obtained by this extended KWC model are compared to existing results in the literature obtained by the original KWC phase-field model. The procedure of the parameter estimation for a simple isotropic case (no orientation dependence of the surface energy and kinetic parameters) is suggested. The ability of the model to describe the grain boundaries with low misorientation and to incorporate the grain boundary diffusion with the impurity segregation is discussed.