In this paper, a new self-organizing fuzzy neural network model is presented which is able to learn and reproduce different sequences accurately. Sequence learning is important in performing skillful tasks, such as writing and playing piano. The structure of the proposed network is composed of two parts: 1-sequence identifier which computes a novel sequence identity value based on initial samples of a sequence, and detects the sequence identity based on proper fuzzy rules, and 2-sequence locator, which locates the input sample in the sequence. Therefore, by integrating outputs of these two parts in fuzzy rules, the network is able to produce the proper output based on current state of the sequence. To learn the proposed structure, a gradual learning procedure is proposed. First, learning is performed by adding new fuzzy rules, based on coverage measure, using available correct data. Next, the initialized parameters are fine-tuned, by gradient descent algorithm, based on fed back approximated network output as the next input. The proposed method has a dynamic structure which is able to learn new sequences online. The proposed method is used to learn and reproduce different sequences simultaneously which is the novelty of this method.