An antitrapping current scheme for quantitative phase-field model [A. Karma, Phys. Rev. Lett. 87, 115701 (2001)] is extended to solidification process in a dilute binary alloy system involving diffusion in the solid. It is demonstrated in an asymptotic analysis that in the case of an arbitrary value of the solid diffusivity, five types of constraints exist between interpolating functions used in the phase-field model, which need to be satisfied simultaneously to eliminate all anomalous interface effects. Then, the authors present an appropriate form of the antitrapping current term for the two-sided case to remove all the spurious effects. The convergence test of the output with respect to the interface thickness was carried out for the isothermal dendrite growth process, which demonstrates an excellent performance of the present model.