All-dielectric metasurfaces have attracted attention for highly efficient visible light manipulation. So far, however, they are mostly passive devices, while those allowing dynamic control remain a challenge. A highly efficient tuning mechanism is immersing the metasurface in a birefringent liquid crystal (LC), whose refractive index can be electrically controlled. Here, an all-dielectric tunable metasurface is demonstrated based on this concept, operating at visible frequencies and based on TiO2 nanodisks embedded in a thin LC layer. Small driving voltages from 3~5 V are sufficient to tune the metasurface resonances, with an associated transmission modulation of more than 65%. The metasurface optical responses, including the observed electric and magnetic dipole resonance shifts as well as the interfacial anchoring effect of the LC induced by the presence of the nanostructures, are systematically discussed. The dynamic tuning observed in the transmission spectra can pave the way to dynamically tunable metasurface devices for efficient visible light modulation applications.