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The successful demonstration of Q-switched and mode-locked fiber-laser operations using a topological insulator (TI) as saturable absorber (SA) has opened an application window besides TI's originally expected features. However, to date, all-solid-state mode-locked lasers base on TISAs are still unavailable and became a desired goal not only due to their application as light sources, but also because of providing a way for deeper investigation of the nature of ultrafast dynamics present in TISAs. In this paper, the realization of a continuous-wave mode-locked all-solid-state laser with a repetition rate of around 1 GHz is reported using a high-quality TI SA mirror (TI-SAM) with ultralow saturation intensity, fabricated by a spin coating-co-reduction approach. An output power of 180 mW and pulse duration of 8 ps are observed. In addition, a 61 dB pulse-train quality from the radio frequency spectrum of mode-locked operation prove the feasibility of the proposed laser. To the best of our knowledge, this is the first experimental demonstration of a mode-locked solid-state laser based on TIs. In addition, this paper shows that the use of TISAs is a promising option for the realization of scaling solid-state mode-locked lasers with higher repetition rates, reaching order of GHz.