The invention discloses an electromagnetic riveting press suitable for large-diameter rivets and a press riveting method thereof, and relates to an electromagnetic riveting press and a press riveting method thereof. A composite structure is riveted by adopting the large-diameter rivets, and the problem of interference quantity and higher electromagnetic riveting requirement operation level are difficultly controlled by adopting hammer riveting and press riveting. An upper riveting die and a stress wave modulator of an electromagnetic riveting gun are jointed or manufactured into a whole; the electromagnetic riveting gun is arranged on a slipway on a horizontal arm; a riveting gun stroke control power source is connected with a control box; the control box is connected with a charge control signal input end of a low-voltage electromagnetic riveting device and a high-voltage pulse generator; the high-voltage pulse generator is connected with a discharge control signal input end of the low-voltage electromagnetic riveting device; positive and negative output ends of discharge signals are connected with two ends of a coil of the electromagnetic riveting gun; and the riveting gun stroke control power source drives the electromagnetic riveting gun to move downwards, a capacitor bank is charged and discharged, and a driving plate is subjected to the axial downward pulse loading effect so that an extended part of a nail bar forms an upset head. The electromagnetic riveting press is used for riveting structural members by the large-diameter rivets.