An iDdQ(q-1) MRT LB model with external force term is proposed with multi-scale expansion and inverse design method. It recovers to incompressible Navier-Stokes equation with external force term under low Mach number assumption. With simulations of Poiseuille flow, pulsatile flow in a three-dimensional square channel, and two-dimensional Taylor vortex flow in a square box, it is found that numerical results are in good agreement with analytical solutions. In addition, spatial accuracy of the model reaches second order, which verifies effectiveness of the model in simulating steady and unsteady incompressible flows driven by external forces.