© 2019 Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Sciences and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd. One of the main problems in particle physics is to understand the origin and nature of dark matter. An exciting possibility is to consider that dark matter belongs to a new complex but hidden sector. In this paper, we assume the existence of a strongly interacting dark sector consisting of a new scalar doublet and new vector resonances, in accordance with the model recently proposed by our group. Since it was found in the previous work that it is very challenging to find the new vector resonances at the LHC, here we study the possibility of finding them at the future Compact Linear Collider (CLIC) running at √ s = 3 TeV. We consider two distinct scenarios. In the first, when the non-standard scalars are heavy, the dark resonance is intense enough to make its discovery possible at CLIC when the resonance mass is in the range [2000, 3000] GeV. In the second scenario, when the non-standard scalars are light, the new vector boson is too broad to be recognized as a resonance, and is not detectable except when the mass of the scalars is close to (but smaller than) half of the resonance mass and the scale of the dark sector is high. In all positive cases, less than a tenth of the maximum integrated luminosity is needed to reach the discovery level. Finally, we also comment on the mono- production.