An auto-unlock assembly for a tubular lock has a rotating pipe, a rotating mount, a positioning board, a rotating spindle, a limiting mount, an retaining board and a limiting spring. The rotating pipe has a through hole. The rotating mount is connected to the rotating pipe and has two connecting wings. The positioning board is mounted in the rotating mount and has a body and two positioning wings. The rotating spindle is rotatably mounted through the rotating pipe and the positioning board via the rotating mount and has two protruding blocks. The limiting mount is mounted around the rotating spindle and has an acting face, a limiting recess and two mounting recesses. The retaining board is mounted around the rotating spindle, abuts the limiting mount and has a base and two protruding lugs. The limiting spring is mounted around the rotating spindle and abuts the retaining board.