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As a mesoscopic computational method, the lattice Boltzmann method (LBM) has been widely applied in engineering physics areas. When it is used for non-Newtonian fluids, the greatest challenges are instability and poor accuracy. To solve the problem, an idea is introduced based on the multi-relaxation-time lattice Boltzmann method (MRT LBM), which is applicable to common non-Newtonian fluids. The non-Newtonian effect is considered a special external force term, whereas the specific forms of forces vary for different types of non-Newtonian fluids. The detailed forms of power-law fluids, Bingham fluids and Herschel–Bulkley fluids are explored. To validate the feasibility of the method, theoretical solutions of Poiseuille flow are used to compare with numerical solutions. Furthermore, the effects of potential factors on the relative errors are analyzed. Finally, the proposed method is used to solve the classical lid-driven cavity flow with high Reynolds numbers, which is frequently encountered in practical applications. The analysis will further validate the method. The simulations show that both initial yielding-stress and power-index have important effects on the flow.