In this work, an approach for performing mesh adaptation in the numerical simulation of two-dimensional unsteady flow with moving immersed boundaries is presented. In each adaptation period, the mesh is refined in the regions where the solution evolves or the moving bodies pass and is unrefined in the regions where the phenomena or the bodies deviate. The flow field and the fluid–solid interface are recomputed on the adapted mesh. The adaptation indicator is defined according to the magnitude of the vorticity in the flow field. There is no lag between the adapted mesh and the computed solution, and the adaptation frequency can be controlled to reduce the errors due to the solution transferring between the old mesh and the new one. The preservation of conservation property is mandatory in long-time scale simulations, so a P1-conservative interpolation is used in the solution transferring. A nonboundary-conforming method is employed to solve the flow equations. Therefore, the moving-boundary flows can be simulated on a fixed mesh, and there is no need to update the mesh at each time step to follow the motion or the deformation of the solid boundary. To validate the present mesh adaptation method, we have simulated several unsteady flows over a circular cylinder stationary or with forced oscillation, a single self-propelled swimming fish, and two fish swimming in the same or different directions. Copyright © 2012 John Wiley & Sons, Ltd.