Flexible and broadband microwave-absorbing structures have attracted significant attention in electromagnetic (EM) science. Although previous studies have demonstrated the potential of flexible microwave-absorbing structures using thin dielectric substrates or flexible materials, the need for broadband and flexible microwave-absorbing structures remains largely unmet, especially those that can be stretched to adapt to complex surfaces. In this article, a novel design concept of a stretchable meta-substrate comprising rigid pyramidal substrates and soft hinges is proposed, which operates as a dielectric substrate and a structural support for the metastructure. The proposed flexible and broadband microwave-absorbing metastructure is composed of a pyramidal microwave-absorbing unit and a stretchable meta-substrate, which exhibits a reflection coefficient lower than −20 dB from 2.2 to 20 GHz under normal incidence. By overcoming the mechanical and electromagnetic limitations of previous efforts with a soft material-based microwave-absorbing structure, the proposed metastructure can be stretched under 40% strain, while the −10 dB reflection coefficient spectrum only shifts by 1.1 GHz. Furthermore, the proposed metastructure exhibits stable absorption properties for EM wave irradiation with both transverse electric and transverse magnetic polarizations, even at an oblique incident angle of up to 70°. As a proof of concept, the proposed metastructure is conformally pasted on the unmanned aerial vehicle surface, and the maximum radar cross section reduction of the proposed metastructure is 30.5 dB larger than that of a conventional device. The fabricated sample can be readily applied for carrying and deployment, with potential applications in the fields of EM stealth as well as EM anti-interference.