A control object can be stopped at a target position with high precision by decelerating braking performed by decreasing a control speed of a speed controller and by decelerating braking performed by braking operation of a brake device. A positioning apparatus includes a rotation detecting sensor S coupled to a rotary shaft for rotating or rectilinearly driving a control object. A normal-reverse rotation discriminating circuit DD for discriminating normal rotation of the rotary shaft from reverse rotation thereof. A first decelerating position memory B1 for holding at least one decelerating position where low-speed driving operation is to be started, and second decelerating position memory B2 for holding at least one decelerating position where braking operation is to be started. First and second decelerating position comparators CP1 and CP2 for comparing counted values with first and second decelerating positions in the first and second decelerating position memories B1 and B2. A rotation speed controller for rotating the rotary shaft of the rotation driving source at a constant speed. Driving controller DR for outputting a decelerating signal for changing a control speed to the rotation speed controller on the basis of a result of comparison output from the first decelerating position comparator, a brake device decreasing at least the rotation speed as a result of comparison output from the second decelerating position comparator, and brake control means BR for outputting a brake signal to the brake device.