Abstract: Based on the modeling idea of non-lineal auto-regressive moving average model and feedforward neural network, the new dynamic recu rsive neural network with the input and output neuron recursion is proposed. Based on the different combined ways to the genetic algorithm, evolutionary strategy and auto-optimal Back Propagation algorithm, the two fully automatic design a lgorithms for the dynamic recursive neural network are also advanced to realize high learning speed and simultaneous optimization learning of network structure, weights, and self feedback parameters. The result of the real applications hows that the new network and design algorithms are effective.