The propagation properties of Si-based all-dielectric metamaterials (ADMs) structures were investigated systematically, taking into account the effects of structural parameters, operation frequencies, and graphene Fermi levels. The results manifested that ADMs indicated sharp resonant curves with large Q-factors of more than 60, and a figure of merit of approximately 20. Compared with that of thin metal metamaterial counterparts, the thickness of ADMs (in the range of tens of micrometers) required to excite obvious resonant curves was much larger. By introducing an asymmetrical structure, an obvious Fano-resonant peak was observed, which also became stronger with increasing asymmetrical degree. In addition, by unitizing a uniform graphene layer, the Fano-resonant curves can be flexibly modulated over a wide range, and the amplitude-modulation depth of the Fano peak was approximately 40% when the Fermi level varied in the range of 0.01-1.0 eV. These results are very useful for the design of high Q-factor dielectric devices in the future (e.g., biosensors, modulators, and filters).