A neural network based control system Self-Organizing Neural-Net-Controller System: has been developed as an adaptive control system for Autonomous Underwater Vehicles (AUVs). In this paper, an on-line adaptation method is proposed to improve the time-consuming adaptation process of the original SONCS. The Imaginary Training can be realized by a parallel structure which enables the SONCS to adjust the controller network independently of actual operation of the controlled object. The SONCS is divided into two separate parts: the Real-World Part where the controlled object is operated according to the objective, and the Imaginary-World Part where the Imaginary Training is carried out. In order to adjust the controller network by the Imaginary Training, it is necessary to introduce a forward model network which can generate simulated state variables without involving actual data. A neural network Identification Network which has a specific structure to simulate the behavior of dynamical systems is proposed as the forward model network. The effectiveness of the Imaginary Training is demonstrated by applying to the heading keeping control of an AUV Twin-Burger. It is shown that the SONCS adjusts the controller network-through on-line processes in parallel with the actual operation. >