The dynamic behavior of the concentration field in crystallization is investigated by considering the coupling of the bulk concentration field and interfacial kinetics. It is shown that the concentration field may become unstable for perturbations with certain wavelength. When instability occurs, the physical environment in front of the growing interface will fluctuate and the interfacial growth mode will be affected accordingly. We suggest that our analysis can be used to interpret some spatial-temporal instabilities observed in crystallization.