Simple cycle reservoir is a classic work in reservoir structure design, and has good performance in tasks such as discrete dynamical system prediction and time series classification. However, the overly simple reservoir structure weakens its ability to model the complex systems such as chaotic systems. A minimum complexity interaction echo state network (MCI-ESN) is proposed in this paper to overcome the shortcomings of simple cycle reservoir. MCI-ESN consists of two identical simple cycle reservoirs which are interconnected by only two neurons for reducing the connection redundancy and improve connection efficiency. A sufficient condition is given to guarantee that the MCI-ESN model has the echo state property. Several numerical experiments, including multivariable chaotic time series prediction and time series classification, are used to verify the effectiveness of the proposed method.