Wavefront shaping based on digital optical phase conjugation (DOPC) focuses light through or inside scattering media, but the low speed of DOPC prevents it from being applied to thick, living biological tissue. Although a fast DOPC approach was recently developed, the reported single-shot wavefront measurement method does not work when the goal is to focus light inside, instead of through, highly scattering media. Here, using a ferroelectric liquid crystal based spatial light modulator, we develop a simpler but faster DOPC system that focuses light not only through, but also inside scattering media. By controlling 2.6 × 105 optical degrees of freedom, our system focused light through 3 mm thick moving chicken tissue, with a system latency of 3.0 ms. Using ultrasound-guided DOPC, along with a binary wavefront measurement method, our system focused light inside a scattering medium comprising moving tissue with a latency of 6.0 ms, which is one to two orders of magnitude shorter than those of previous digital wavefront shaping systems. Since the demonstrated speed approaches tissue decorrelation rates, this work is an important step toward in vivo deep-tissue non-invasive optical imaging, manipulation, and therapy.