An approach for performing mesh adaptation in numerical simulation of two-dimensional unsteady flow is presented. A predictor-corrector step is introduced in the process of "solving flow equations-adjusting mesh". At first, flowfield during an adaptation period is precomputed to produce a posteriori error estimate. Then, an indicator for mesh adaptation in which solution progression is taken into account is constructed. Adaptive mesh is generated through multi-level reflnement/unrefinement. Finally, unsteady flow field is recomputed on the new adaptive mesh. In each adaptation period, mesh is refined in regions where solution evolves and is unrefined in regions where phenomena deviate since the last adaptation. A non-boundary-conforming method named local domain-free discretization is employed to solve flow equations. To validate the method, we simulated unsteady flows over a circular cylinder and a self-propelled swimming fish.