This paper is to present map building of mobile robot using RFID (Radio Frequency Identification) technology and ultrasonic sensor. For mobile robot to perform map building, the mobile robot needs its localization and accurate driving in space. In this reason, firstly, kinematic modeling of mobile robot under non-holonomic constrains is introduced. Secondly, based on this modeling, a tracking controller is designed for tracking a given path based on backstepping method using Lyapunov function. The Lyapunov function is also introduced for proving the stability of the designed tracking controller. Thirdly, 2D map building is performed by RFID system, mobile robot system and ultrasonic sensors. The RFID mobile robot system is composed of DC motor, encoder, ultra sonic sensor, digital compass, RFID receiver and RFID antenna. Finally, the path tracking simulation results and map building experimental results are presented to show the effectiveness of the designed controller.