The invention discloses an earth pressure TBM double-mode double-support heading machine and a construction method. The earth pressure TBM double-mode double-support heading machine comprises a cutterhead, a shield body, a belt conveyor, a main drive used for driving the cutterhead, a propelling part used for pushing the cutterhead to move, a central screw conveyor used in a TBM mode, a shotcrete anchor support assembly used in the TBM mode, a bottom screw conveyor used in an earth pressure mode and a segment erector are used in the earth pressure mode. The central screw conveyor and the bottom screw conveyor are arranged in a crossed mode, a screw shaft of the central screw conveyor and a screw shaft of the bottom screw conveyor can alternatively move to a working position, and the belt conveyor is positioned at the tail parts of the central screw conveyor and the bottom screw conveyor. According to the earth pressure TBM dual-mode and dual-support tunneling machine, earth pressure and TBM dual-mode propelling is adopted, higher geological adaptability is achieved, the central screw conveyor and the bottom screw conveyor are arranged in a crossed mode, structural interference is avoided, one of the central screw conveyor and the bottom screw conveyor can be selected to move to the working position, mode conversion is convenient, and operability is high.