Recurrent neural networks have interesting properties and can handle dynamic information processing unlike ordinary feedforward neural networks. However, they are generally difficult to use because there is no convenient learning scheme. In this paper, a recursive learning scheme for recurrent neural networks using the simultaneous perturbation method is described. The detailed procedure of the scheme for recurrent neural networks is explained. Unlike ordinary correlation learning, this method is applicable to analog learning and the learning of oscillatory solutions of recurrent neural networks. Moreover, as a typical example of recurrent neural networks, we consider the hardware implementation of Hopfield neural networks using a field-programmable gate array (FPGA). The details of the implementation are described. Two examples of a Hopfield neural network system for analog and oscillatory targets are shown. These results show that the learning scheme proposed here is feasible.