Broadband acoustic absorber via a structure with sub-wavelength thickness is of great and continuing interest in research and engineering communities. To broaden the absorption band of acoustic absorbers, common methods often involve using septum to create a double-layer structure or replacing cavity walls with flexible materials. However, such approaches require strict restrictions of thickness and structure design for the absorbers. This work presents a metamaterial design method that uses an external frame to construct double resonant metamaterials, effectively improving broadband sound absorption performance. Specifically, this method can be decoupled from the design of original cavity-type absorber structure and external frame. The absorption performance is significantly improved by adding an external frame to wrap around a cavity-type acoustic absorber structure with air. Furthermore, utilizing the coaction of cascade coupling and external frame, the average absorption ratio of the metamaterial in high-frequency domain (above 2000 Hz) can be improved by six times. Since this structural design broadens the absorption band without changing structural parameters of the original absorber, it has potentials to be applied in various engineering fields.