In this paper, a tunable terahertz dielectric metasurfaces consisting of split gap bars in the unit cell is proposed and theoretically demonstrated, where the sharp high-quality Fano resonance can be achieved through excitation of quasi-bound states in the continuum (quasi-BIC) by breaking in-plane symmetry of the unit cell structure. With the structural asymmetry parameter decreasing and vanishing, the calculated eigenmodes spectra demonstrate the resonance changes from Fano to symmetry-protected BIC mode, and the radiative quality factors obey the inverse square law. Moreover, combining with graphene monolayer and strontium titanate materials, the quasi-BIC Fano resonance can be tuned independently, where the resonance amplitude can be tuned by adjusting the Fermi level of graphene and the resonance frequency can be tuned by controlling the temperature of strontium titanate materials. The proposed structure has numerous potential applications on tunable devices including modulators, switches, and sensors.