In this manuscript, we pioneer an efficient indoor mobile robot navigation system using signal strength of a customized RFID system. The RFID reader is mounted on the robot and a set of RFID tags are attached to 3-D points which are known as targets to be reached by the mobile robot in an indoor workspace. First, the direction of a current target is estimated through received signal strength (RSS) measurements of the customized RFID reader. The robot's current orientation is updated to head approximately towards the target. It then applies necessary actions to its actuator to reach the current target. The path generated by the robot is better estimated using a conventional stochastic filter called Extended Kalman Filter (EKF). The customized RFID reader architecture is simulated using the comprehensive electromagnetic commercial software, FEKO. The proposed navigation system is evaluated through a number of computer simulations. It is shown through these simulations that a mobile robot has the ability to successfully navigate to reach a set of pre-defined target points in an indoor environment regardless of the 3-D positions of the RFID tags.