A new approach is proposed to accelerate the convergence of the Lattice Boltzmann method for steady-state problems. The proposed approach uses an adaptive relaxation frequency to accelerate the convergence by assigning more weight to selected parts of the standard algorithm corresponding to different phases of the convergence to the steady-state solution. The proposed algorithm is simple, straightforward and does not impose any additional computational cost to the standard algorithm. Different simulation cases are presented with the corresponding speedup. Finally, guidelines for the selection of the optimal adaptation parameters are presented.