A key challenge in long-duration modelling of ocean waves or wave-structure interactions in numerical wave tanks(NWT) is how to effectively absorb undesirable waves on the boundaries of the wave tanks. The self-adaptive wavemaker theory is one technique developed for this purpose. However, it was derived based on the linear wavemaker theory, in which the free surface elevation and the motion of the wavemaker are assumed to be approximately zero. Numerical investigations using the fully nonlinear potential theory based Quasi Arbitrary Lagrangian Eulerian Finite Element Method (QALE-FEM) suggested that its efficiency is relatively lower when dealing with nonlinear waves, especially for shallow water waves due to three typical issues associated with the wave nonlinearity including (1) significant wavemaker motion for extreme waves; (2) the mean wave elevation (i.e. the component corresponding to zero frequency), leading to a constant velocity component, thus a significant slow shift of the wavemaker; (3) the nonlinear components, especially high-order harmonics, may significantly influence the wavemaker transfer functions. The paper presents a new approach to numerically implement the existing self-adaptive wavemaker theory and focuses on its application on the open boundary, where all incident waves are expected to be fully absorbed. The approach is implemented by the NWT based on the QALE-FEM method. A systematic numerical investigation on uni-directional waves is carried out, following the corresponding validation through comparing the numerical prediction with experimental data for highly nonlinear shallow water waves.