The Koopman operator provides a method for the global linearization of nonlinear dynamical systems. When the system states cannot be obtained accurately or only image observations are available, extending the Koopman operator for representing the dynamic evolution through image observations is of great importance in fields such as robotics. This paper introduces HDKI, a deep Koopman framework with a hierarchical structure for dynamical systems image observations. It first generates an embedded representation containing spatial structure, and then learns the Koopman representation within this embedded space. In addition, a spatio-temporal feature extraction module is used to learn the latent states of the Koopman representation. Compared to previous methods, the hierarchical structure of HDKI better handles the spatio-temporal features of image sequences, which helps to expand the application scenarios of deep Koopman methods. We collected data in the classic simulation environment Cartpole of Open AI Gym and conducted experimental tests to verify the effectiveness of the proposed approach. The experiments show that our approach can learn effective Koopman representations with good predictive performance at a lower latent state dimension compared to previous methods.