An adaptive model reduction method is proposed for linear time-invariant systems based on the continuous-time rational orthogonal basis (TakenakaMalmquist basis). The method is to find an adaptive approximation in the energy sense by selecting optimal points for the rational orthogonal basis. The stability of the reduced models holds, and the steady-state values of step responses are kept to be equal. Furthermore, the method automatically ensures the reduced system to be in the Hardy space H2. The existence of the best approximation in the Hardy space H2 by n Blaschke forms is proved in the proposed approach. The effectivity of this method is illustrated through three well-known examples.