Active devices play a critical role in modern electromagnetic and photonics systems. To date, the epsilon (ε)-near-zero (ENZ) is usually integrated with the low Q-factor resonant metasurface to achieve active devices, and enhance the light-matter interaction significantly at the nanoscale. However, the low Q-factor resonance may limit the optical modulation. Less work has been focused on the optical modulation in the low-loss and high Q-factor metasurfaces. Recently, the emerging optical bound states in the continuum (BICs) provides an effective way for achieving high Q-factor resonators. In this work, we numerically demonstrate a tunable quasi-BICs (QBICs) by integrating a silicon metasurface with ENZ ITO thin film. Such a metasurface is composed of five square holes in a unit cell, and hosts multiple BICs by engineering the position of centre hole. We also reveal the nature of these QBICs by performing multipole decomposition and calculating near field distribution. Thanks to the large tunability of ITO's permittivity by external bias and high-Q factor enabled by QBICs, we demonstrate an active control on the resonant peak position and intensity of transmission spectrum by integrating ENZ ITO thin films with QBICs supported by silicon metasurfaces. We find that all QBICs show excellent performance on modulating the optical response of such a hybrid structure. The modulation depth can be up to 14.8 dB. We also investigate how the carrier density of ITO film influence the near-field trapping and far-field scattering, which in turn influence the performance of optical modulation based on this structure. Our results may find promising applications in developing active high-performance optical devices.