Among different phase structures in immiscible polymer blends, the cocontinuous phase structure is considered to be advantageous for load transfer and achieving good mechanical properties. Due to the presence of an interpenetrating interface, phase coarsening naturally occurs during melt processing of cocontinuous polymer blends, and harness of the coarsening kinetics is important for structural control. Existing models for phase coarsening are mostly founded on the basis of scaling or dimensional analysis while computational models embodying more realistic phase geometries are demanded. In this paper, we present a two-step computational approach for prediction of the coarsening kinetics. First, a phase-field transport equation is solved to establish an initial phase geometry. Second, a moving-boundary flow model is implemented to solve the hydrodynamic problem. Case studies are presented both in 2D and in 3D domains. An empirical model on the basis of fractional calculus is also proposed to fit the computational results. Once verified by experimental data, this approach can provide an integrated tool for assisting in the processing of cocontinuous polymer blends where phase coarsening is of concern.