<p>Considering the available space and the lightweight design of the control device, the pendulum tuned mass damper with inerter (PTMDI) has been identified as the most promising control equipment for dissipating the dynamic responses of wind turbine towers. To enhance the vibration dissipation performance of conventional PTMDI, a geometrical nonlinearity property of non-orthogonal spring elements is integrated into this control device to develop a nonlinear PTMDI, which is referred to as PTMDI equipment with geometrical nonlinearity (PTMDI-GN) in this paper. The nonlinear dynamic model of a wind turbine tower equipped with PTMDI-GN equipment, as well as the analytical harmonic response of PTMDI-GN control system, are derived to determine the optimal design parameters of PTMDI-GN. The nonlinear vibration suppression and performance enhancement are comparatively analyzed alongside conventional control devices. The comparison results indicate that PTMDI-GN outperforms the PTMD and conventional linear PTMDI equipment in bidirectional vibration dissipation competence of wind turbine towers by over 10.7% and 4.9% under the wind loads, respectively. Also, movement strokes of PTMDI-GN are smaller than those of PTMD and conventional PTMDI, showing that it has exploitable potential in vibration suppression and performance enhancement of wind turbine towers.</p>