The problem of nonlinear Landau damping of helicon waves in dusty plasma in particular emphasis to the acceleration of soliton is presented here. This in the framework of a collisionless, anisotropic homogeneous dusty plasma in one dimension, can be well described by two coupled dynamical equations of the generalized Zakharov type, with one extra nonlocal term coming from Landau damping. Nonlinear-nonlocal term gives rise to essential contributions relative to the local term. Then under different conditions, kinetic nonlinear Schrödinger equation is constructed and nonlinear decrement is obtained for two cases. It is noticed that the time dependant term in the ponderomotive force plays a significant role for this kind of damping. Additionally, it is shown that nonlinear Landau damping leads to the amplitude modulation of dust helicon waves, further modulational instability, and maximal growth rate is obtained when the group velocity of the helicon wave reaches the dust-acoustic speed. It is demonstrated that how the nonlinear Landau damping leads to the acceleration of soliton, which is eventually slowed down after transferring some of its energy to the wave. Emission of dust-acoustic wave by accelerated soliton is discussed briefly.