To provide a simple numerical formulation based on fixed grids, a wavelet element method for fluid–solid modelling is introduced in this work. Compared with the classical wavelet finite element method, the presented method can potentially handle more complex shapes. Considering the differences between the solid and fluid regions, a damping-like interface based on wavelet elements is designed, in order to ensure consistency between the two parts. The inner regions are constructed with the same wavelet function in space. In the time and spatial domains, a partitioned approach based on Jacobi iteration is combined with the pseudo-parallel calculation method. Numerical convergence analyses show that the method can serve as an alternative choice for fluid–solid coupling modelling.