In this study, a multi-relaxation time lattice Boltzmann model for shallow water in a curvilinear coordinate grid is developed using the generalized form of the interpolation supplemented lattice Boltzmann method. The Taylor-Colette flow tests show that the proposed model enjoys a second order accuracy in space. The proposed model is applied to three types of meandering channels with 180°,90° and 60° consecutive bends. The numerical results demonstrate that the simulated results agree well with previous computational and experimental data. In addition, the model can achieve the acceptable accuracy in terms of the water depth and the depth-averaged velocities for shallow water flows in curved and meandering channels over a wide range of bend angles.