Due to the influence of model deviation and system disturbance, it is difficult to obtain accurate state estimation for complex systems, and generally only the interval of the state can be determined. That is, the interval observer can be designed. However, it is difficult to obtain good estimation results by considering a single performance interval observer. An interval observer approach with $H_2$/H_∞ performance is designed. Based on the obvious relationship among real states, estimated states and estimated errors, the interval hull of errors is calculated and the interval estimation of real states is represented by the combination of estimated states and the upper and lower bounds of errors. Then, anti-interference and robustness of observer are efficiently improved by introducing the smallest mixed $H_2$/H_∞ norm constraint. Finally, an example is presented to demonstrate the effectiveness of the proposed method. The result shows that the proposed $H_2$/H_∞ interval estimation method has better estimation performance for the continuous stirred tank reactor and is convenient to design and implement the following control strategies.