The paper principally describes the design of an artificial neural network using flexible sigmoid unit functions (FSUFs), referred to as flexible sigmoid function networks (FSFNs), to achieve both a high flexibility and a high learning ability in neural network structures from a given set of teaching patterns. An FSFN can generate an appropriate shape of the sigmoid function for each of the individual hidden- and output-layer units, in accordance with the specified inputs, desired output(s) and applied system. The paper proposes a learning method in which not only connection weights but also the sigmoid functions may be adjusted. The learning algorithm is derived by using the well known back-propagation algorithm. To demonstrate the validity of the proposed method, we apply the FSFN to the construction of a self-tuning computed torque controller for a two-link manipulator. It is then shown that the controller based on the FSFN gives a better control performance than that based on the traditional neural network.