Phase-field models provide a way to model fluid interfaces as having finite thickness; the interface between two immiscible fluids is treated as a thin mixing layer across which physical properties vary steeply but continuously. One of the main challenges of this approach is in resolving the sharp gradients at the interface. In this paper, moving finite-element methods are used to simulate interfacial dynamics of two-phase viscoelastic flows. The finite-element scheme can easily accommodates complex flow geometry and the moving mesh strategy can cluster more grid points near the thin interfacial areas where the solutions have large gradients. A diffused monitor function is used to ensure high quality meshes near the interface. Several numerical experiments are carried out to demonstrate the effectiveness of the moving mesh strategy.