A recess is defined in one of the top tube, the down tube and the seat tube of a bicycle frame and a power supply unit is engaged with the recess. The power supply unit includes an engaging frame engaged with the recess and a battery is removably engaged with a main space defined in the engaging frame. The engaging frame includes a chamber defined in an end thereof and a control box is received in the chamber so as to be electrically connected with the control box. The top surface of the battery is in flush with the one of the top tube, the down tube and the seat tube. An ON/OFF switch is installed on a top of the engaging frame and an indication bulb is installed on a top of the battery for convenience of observation by the user.