Obtaining accurate channel state information (CSI) is crucial and challenging for multiple-input multiple-output (MIMO) wireless communication systems. Conventional channel estimation method cannot guarantee the accuracy of mobile CSI while requires high signaling overhead. Through exploring the intrinsic correlation among a set of historical CSI instances randomly obtained in a certain communication environment, channel prediction can significantly increase CSI accuracy and save signaling overhead. In this paper, we propose a novel channel prediction method based on ordinary differential equation (ODE)-recurrent neural network (RNN) for accurate and flexible mobile MIMO channel prediction. Differing from existing works using sequential network structures for exploring the numerical correlation between observed data, our proposed method tries to represent the implicit physics process of path responses changing by specially designed continuous learning network with ODE structure. Due to the targeted design of learning network, our proposed method fits the mathematics feature of CSI data better and enjoy higher network interpretability. Experimental results show that the proposed learning approach outperforms existing methods, especially for long time interval of the CSI sequence and large channel measurement error.