We investigated the dynamic competition crystallization and phase separation in a dynamically asymmetric blend of poly(methly methacrylate) (PMMA) and poly(ethylene oxide) (PEO). Because of a large difference in glass transition dynamics is slowed down and can be observed in more detail. There is a morphological inversion from spherulitic to concentric ring patterns by adjusting the quench depth. Under deep quench, phase separation tends to be enhanced by the large concentration deviation at the growth interface of crystals, and propagates outward with convective concentration waves. Meanwhile, short needle-like crystals appear in the phase separated domains, compared with long crystal strips in a spherulitic pattern. A general dynamic competition model is proposed to qualitatively interpret the complex interplay between crystallization and phase separation. On the basis of this model, various morphologies are observed and predicted.