Highly tunable electromagnetically induced transparency (EIT) with high-quality-factor (Q-factor) excited by combining with the quasi-bound states in the continuum (quasi-BIC) resonances is crucial for many applications. This paper describes all-dielectric metasurface composed of silicon cuboid etched with two rectangular holes into a unit cell and periodically arranged on a SiO2 substrate. By breaking the C2 rotational symmetry of the unit cell, a high-Q factor EIT and double quasi-BIC resonant modes are excited at 1224.3, 1251.9 and 1299.6 nm with quality factors of 7604, 10064 and 15503, respectively. We show that the EIT resonance is caused by destructive interference between magnetic dipole resonances and quasi-BIC dominated by electric quadrupole. Toroidal dipole (TD) and electric quadrupole (EQ) dominate the other two quasi-BICs. The EIT window can be successfully modulated with transmission intensity from 90% to 5% and modulation depths ranging from -17 to 24 dB at 1200-1250 nm by integrating the metasurface with an epsilon-near-zero (ENZ) material indium tin oxide (ITO) film. Our findings pave the way for the development of applications such as optical switches and modulators with many potential applications in nonlinear optics, filters, and multichannel biosensors.