The invention discloses a three-phase converter and a control method and device thereof. The method comprises the following steps of: obtaining phase angles of current and voltage vectors of a dq axis; obtaining the voltage of the dq axis in the current period according to the given current of the dq axis, the current of the dq axis and the amplitude limiting voltage of a first dq axis in the lastperiod; obtaining a harmonic voltage of the dq axis in the current period according to the given current of the dq axis, the current of the dq axis and the amplitude limiting voltage of a second dq axis in the last period; obtaining a compensation voltage of a dead zone of the dq axis in the current period according to the phase angle of the voltage vector and the given current of the dq axis, and performing accumulation of the voltage of the dq axis, the harmonic voltage of the dq axis and the compensation voltage of the dead zone of the dq axis in the current period to obtain an expected voltage of the dq axis, and performing voltage amplitude limiting processing for the expected voltage of the dq axis to obtain an actual output voltage of the dq axis and control the three-phase converter so as to obtain the amplitude limiting voltages of the first dq axis and the second dq axis in the current period. The method provided by the invention can effectively inhibit the harmonic current,and is fast in the harmonic control response speed and fast in desaturation speed.