A leg press exercise machine comprises: a frame; a seat unit attached to the frame; a press mechanism attached to the frame, the press mechanism including a foot panel and at least one swing link pivotally interconnected with the frame; a resistance-imparting unit operatively connected with the press mechanism; and a resistance coupling mechanism attached to the press mechanism and the resistance-imparting unit. The press mechanism is configured such that the foot panel is movable along a generally longitudinal stroke path between a retracted position and a fully extended position. The resistance-imparting unit provides resistance to the foot panel as it moves from the retracted position to the fully extended position. The resistance coupling mechanism includes a drawing link pivotally interconnected with the swing link and a control link pivotally interconnected with the drawing link and the press mechanism. The control link is further attached to the resistance-imparting unit.