This paper presents a Hybrid filter based Simultaneous Localization and Mapping (SLAM) scheme for a mobile robot to compensate for the Extended Kalman Filter (EKF) based SLAM errors inherently caused by its linearization process. The proposed Hybrid filter consists of a Radial Basis Function (RBF) and EKF which is a milestone for SLAM applications. A mobile robot autonomously explores the environment by interpreting the scene, building an appropriate map, and localizing itself relative to this map. A probabilistic approach has dominated the solution to the SLAM problem, which is a fundamental requirement for mobile robot navigation. The proposed approach, based on a Hybrid filter, has some advantages in handling a robotic system with nonlinear dynamics because of the learning property of the neural networks. The simulation and experimental results show the effectiveness of the proposed algorithm comparing with an EKF based SLAM and Multi Layer Perceptron (MLP) method.