The commutation failure of high voltage direct current (HVDC) systems could lead to unstable operation of the alternating current/direct current (AC/DC) hybrid power grid. The commutation voltage distortion caused by harmonics is a considerable but unclear factor of commutation failure. According to the control switching process of HVDC systems, the commutation voltage-time area method is employed to analyze and reveal the influence mechanism of harmonic components of commutation voltage on first and subsequent commutation failures. Considering the distortion characteristics of AC voltage, a predictive commutation failure suppression strategy considering multiple harmonics of commutation voltage is proposed. In this strategy, the new extinction angle and the zero-crossing offset angle after voltage distortion are calculated considering the harmonic components so as to obtain the compensation margin of the lag trigger angle by combining the correction margin with the voltage change rate. Moreover, the tuning method of parameters of extinction angle and voltage prediction variables are provided. Finally, a case study based on CIGRE standard HVDC system is performed and analyzed by using power systems computer-aided design (PSCAD) software. Compared with the International Council on Large Electric systems (CIGRE) standard test model and traditional commutation failure prevention (CFPREV) control model, the results verify that the proposed strategy can effectively reduce the risk of first and subsequent commutation failures and improve the sensitivity of CFPREV control.