The momentum exchange method has been widely used in lattice Boltzmann simulations for particle-fluid interactions. Although proved accurate for still walls, it will result in inaccurate particle dynamics without corrections. In this work, we reveal the physical cause of this problem and find that the initial momentum of the net mass transfer through boundaries in the moving-boundary treatment is not counted in the conventional momentum exchange method. A corrected momentum exchange method is then proposed by taking into account the initial momentum of the net mass transfer at each time step. The method is easy to implement with negligible extra computation cost. Direct numerical simulations of a single elliptical particle sedimentation are carried out to evaluate the accuracy for our method as well as other lattice Boltzmann-based methods by comparisons with the results of the finite element method. A shear flow test shows that our method is Galilean invariant.