In the previous paper, a structure of feed forward neural network and its learning process were proposed to simulate the dynamic behavior of the controlled object. The network includes two kinds of recurrent connections, i.e., from the output layer to the input layer and from the hidden layer to the input layer. The first connection enables the network to obtain the input state variables from its own outputs and the second one is to keep the influence of the past data in itself. In this paper, the learning process is improved to equip the network with the capability of emulating the dynamic behavior including higher-order finite differences. The proposed network is adopted to the neural-network-based control system called “SONCS : Self-Organizing Neural-net Controller System”, which has been developed as an adaptive control system for underwater robots. The neural network controller in SONCS can be quickly adapted taking advantage of the network's simulating ability. The efficiency of the network is successfully demonstrated through the application to heading keeping control of a versatile robot called “Twin-Burger”.