We have designed an all-dielectric device based on permittivity-asymmetric rectangular blocks on meta-surfaces, yielding multiple Fano resonances with high sensitivity and high figure of merit (FOM) in the near-infrared regime. By introducing different materials to break the permittivity-symmetry, three sharp Fano peaks are generated with high Q-factors arising from the interference between the sub-radiant modes and the magnetic dipole resonance modes. Combining the field distributions and the multipole decomposition in Cartesian coordinates, the resonance modes are analyzed to be magnetic quadrupoles (MQs) and magnetic dipoles (MDs). Furthermore, the dependence on materials and geometric parameters has been studied. The maximal sensitivity, FOM and Q-factor reach 394nm/RIU, 4925 and 14437, respectively. This proposed structure provides a good alternative to geometry-asymmetric meta-surface structures and may be used for multichannel sensing, nonlinear optical devices, and laser.