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A phase-field model has been developed to describe microstructure evolution during intercritical annealing of a commercial DP600 dual-phase steel. The simulations emphasize the interaction between ferrite recrystallization and austenite formation from a cold-rolled pearlite/ferrite microstructure at high heating rates. The austenite-ferrite transformations are assumed to occur under conditions where only carbon partitions between the phases by long-range diffusion. A solute drag model has been integrated with the phase-field model to describe the effect of substitutional alloying elements on the migration of the ferrite/austenite interface. Experimental results including recrystallization and transformation kinetics as well as austenite morphology have been successfully described by carefully adjusting both the austenite nucleation scenario and the interface mobilities.