•The mixed columnar-equiaxed solidification during steel strip feeding in continuous casting was studied.•Steel strip feeding can improves solidification quality by increasing the equiaxed grain percentage.•A mathematical relationship between equiaxed grain percentage and initial temperature and size of strip was established. Feeding a steel strip into a continuous casting (CC) mold is an effective method for improving the internal quality of CC slabs. An alloy experiment and three-phase mixed columnar-equiaxed solidification modeling were used to investigate the solidification structure evolution during the cold strip feeding process. The Euler method was adopted to treat the liquid phase, columnar grain phase, and equiaxed grain phase as continuous phases, and the mass, momentum, energy, and species transport equations of each phase, as well as the equiaxed grain density equation, were solved simultaneously. A comparison of the simulation and experimental results shows that the model can be used for calculating phase transitions, thermal-solute convection, grain deposition, macro-segregation, and the transformation of columnar grains into equiaxed grains in the solidification-melting system, which reveals the inherent relationship between the cold strip parameter and equiaxed grain percentage that is unquantifiable in the experiments. The results show that cold strip feeding improves the solidification structure quality by accelerating nucleation, strengthening convection, and promoting the columnar-equiaxed grain transition (CET). The subcooling nucleation rate around the cold strip first increases to a maximum and then decreases over time. A mathematical relationship between the equiaxed grain percentage and the initial temperature and size of the cold strip was established.