We introduce a novel multiple-relaxation time (modified MRT) Lattice Boltzmann scheme for simulation of confined suspension flow. Via careful tuning of the free eigenvalues of the collision operator we can substantially reduce the error in the so-called hydrodynamic radius. Its performance has been compared to that of the TRT scheme for several benchmark problems. We have found that the optimal value of the free eigenvalue depends on the curvature of the solid–fluid interfaces. Hence, we have investigated suspension flow problems, with confining boundaries of different curvatures. We have found that the modified MRT scheme is better suited for suspension flow in curved confining walls, while the TRT scheme is better for suspension flow confined between planar walls. With both schemes we have investigated problems for confined suspension flows, namely 1) drag forces experienced by spheres flowing in confining flow channels of different cross sections, and 2) the lubrication force between a sedimenting sphere and the end cap of a confining cylindrical capillary.