In this paper, a new identification method for systems with a circulation structure is proposed. The output of the system is strongly correlated with that of the previous circulation period under the influence of the substances circulating in the system. Therefore, the model for such system contains higher order terms, which makes it difficult to identify the system when its circulation period is unknown. To deal with the systems with unknown circulation period, the proposed method utilizes the feature extraction method with l₁-norm optimization technique, which can estimate sparse parameter vector appears in the models with the circulation structure. A numerical simulation is given to show the effectiveness of the proposed method.