River bank retreat and advance are modes of morphological evolution in addition to bed level changes and changes in bed sediment composition. They produce planform changes such as width adjustment and meander bend migration. However, their reproduction in a 2D numerical model still remains a challenge. Defining bank-lines along the nearest grid lines of a rectangular computational grid leads to staircase lines that impede any reasonable determination of the hydraulic loads on the banks. An adaptive curvilinear boundary-fitted grid may seem to solve this problem, but arbitrary bank retreat and advance appear to deform such a grid prohibitively within a few bank-line update steps. We therefore present a new approach in which shifting bank-lines are followed as separate moving objects on a fixed grid, using local immersed-boundary techniques to solve the flow and sediment transport in the vicinity of the bank-lines. This means that the grid itself remains stationary but the flow domain is adapted each (morphological) time step. The use of separate moving objects also gives the opportunity to track bank-lines that are not on the border of the computational domain, but somewhere inside this domain, e.g. the main river channel between floodplains or the channels in an estuary. The immersed-boundary approach with moving bank lines has been implemented in the existing framework of Delft3D, which allows us to reuse all advanced features that are already present in this code, such as advanced bed level updating and sediment transport formulations. The distance and the direction of bank retreat are computed using a simple bank erosion formula, but can be easily extended to incorporate other bank erosion mechanisms. We analyze the performance of this approach for a simple meandering river. The results show that the new approach is capable of reproducing complex river planform changes without grid deformation problems and without the need to employ a very fine grid.