A two zone lens auto-focusing system to be used in a digital still camera includes a picture taking lens, a solenoid to switch the lens focus point between near distance point and far distance point. The CPU or the electronically controlled distance measuring system of the camera having detected the position of the object, it excites the solenoid, and the head of the solenoid is pulled into the solenoid body with a very short stroke, and the arm that is provided on the lens barrel and coupled with the solenoid head is also pulled toward the solenoid body to transfer the movement of solenoid head to the lens barrel, so that the lens focus may be set at either of far position or near position automatically. These members are assembled and form a simple two zone auto-focusing system of digital still cameras.