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The lattice Boltzmann method (LBM) is a potent numerical technique based on kinetic theory. It can effectively simulate the steady-state and unsteady-state flow problems. A multi-domain decomposition strategy is developed for the LBM in order to accelerate the rate of convergence in different domains by the relative error in the different regions of the steady-state flow. In addition, the proposed method can effectively reduce the amount of calculations required and improve numerical stability. Numerical experiments involving both two- and three-dimensional steady-state flows demonstrate drastically improved computational efficiency and superior numerical stability over the popular lattice Bathnagar-Gross-Krook (BGK) model. Moreover, for unsteady-state flow problems, the presented method can also be used to obtain the flow phenomenon of some unsteady-state flows by choosing the suitable parameter.