We theoretically investigate high-order harmonic generation by employing strong-field approximation(SFA) and present a new approach to the extension of the high-order harmonic cutoff frequency via an exploration of the dependence of high-order harmonic generation on the waveform of laser fields.The dependence is investigated via detailed analysis of the classical trajectories of the ionized electron moving in the continuum in the velocity-position plane.The classical trajectory consists of three sections(Acceleration Away,Deceleration Away,and Acceleration Back),and their relationship with the electron recollision energy is investigated.The analysis of classical trajectories indicates that,besides the final(Acceleration Back) section,the electron recollision energy also relies on the previous two sections.We simultaneously optimize the waveform in all three sections to increase the electron recollision energy,and an extension of the cutoff frequency up to Ip+20.26Up is presented with a theoretically synthesized waveform of the laser field. We theoretically investigate high-order harmonic generation by employing strong-field approximation (SFA) and present a new approach to the extension of the high-order harmonic cutoff frequency via an exploration of the dependence of high-order harmonic generation on the waveform of laser fields the dependence is investigated by detailed analysis of the classical trajectories of the ionized electron moving in the continuum in the velocity-position plane. The classical trajectory consists of three sections (Acceleration Away, Deceleration Away, and Acceleration Back), and their relationship with the electron recollision energy is investigated.The analysis of classical trajectories that that, besides the final (Acceleration Back) section, the electron recollision energy also relies on the previous two sections. We simultaneously optimize the waveform in all three sections to increase the electron recollision energy, and an extension of the cutoff frequency up to Ip + 20.26Up is presented with a theoretically dominant waveform of the laser field.