The peritectic reaction process in carbon steel, L+δ→γ, is analyzed by a quantitative phase-field simulation. The calculated moving velocities of γ-L and γ-δ planar interfaces in the isothermal peritectic transformation precisely agree with the corresponding experimental data, which strongly supports the accuracy of the present simulation. The diffusion-controlled peritectic reaction rate or the growing velocity of γ phase along δ-L interface obtained by the present simulation is fairly consistent with the experimentally measured value. This fact indicates that the recent experimental findings can be explained by the diffusion-controlled mechanism. This is in marked contrast to the claims made on the basis of the experimental data and an analytical model that the peritectic reaction is not controlled by the diffusion of carbon.