The strapdown inertial navigation system is usually employed to determine the attitude, velocity and position of an Autonomous Underwater Vehicle (AUV) for its specific advantage of small volume. The navigation accuracy provided by the SINS which employs accelerometers and gyroscopes deteriorates with time. Consequently, an external aiding source such as Global Positioning System (GPS) can be employed to reduce the error growth in the SINS. The GPS aided SINS system provides enhanced positioning accuracy of the AUV compared to that of a stand-alone SINS technique. A new method based on Kalman filtering and RBF neural network to fuse the GPS and the SINS data for an AUV application was presented in this paper. It was proved from the experiments that navigation accuracy was improved substantially between GPS position fixes with the proposed method.