A dog clutch engagement method of an electric four-wheel drive vehicle includes steps of: when dog clutch engagement is requested during driving, determining a target synchronization speed of the input gear to be a sum of an estimated speed and an offset speed of the output gear; operating a drive unit so that an input gear follows the target synchronization speed; when an actual speed of the input gear reaches the target synchronization speed, moving a sleeve to a meeting position at which the sleeve is in contact with the input gear; and when the actual speed of the input gear is synchronized with an actual speed of the output gear, transporting the sleeve to an engagement position at which the input gear and the output gear are coupled.