Based on cellular automaton method, a numerical model was developed for the regular eutectic growth of binary alloy. By coupling with the macro-temperature field and considering the solute diffusion, the constitutional undercooling and the curvature undercooling, modeling of the steady-state lamellar eutectic growth was achieved. A systematic investigation on eutectic growth morphology and lamellar spacing of a model alloy was made under unidirectional solidification conditions with different undercoolings, initial lamellar spacings, temperature gradients and solidification rates. The results reproduced the adjustment of lamellar spacing of two eutectic phases under the interaction between solute diffusion and surface energy by mechanisms of nucleation, lamellar branching, lamellar termination and overgrowth. The simulated results were in agreement with those predicted by the Jackson-Hunt model and experimental results by other researchers. Finally, the model was extended to three dimensional systems, which verified its feasibility of modeling the three-dimensional eutectic growth.