Based on the electromagnetic properties of all-dielectric optical metamaterial, an all-dielectric metasurface of lattice-perturbed nanohole array is proposed to excite a multiple Fano resonance in the near-infrared region. Combined with the group theory, the formation mechanism and evolution law of multiple Fano resonances in this structure when its unit cell is a square lattice configuration and the square lattice symmetry is broken are explored in depth. The results show that double degenerate mode directly excited by the normal incident plane wave is coupled to vertical free-space radiation continuum to form double Fano resonance when unit cell is symmetrical, while the uncoupled non-degenerate modes excited by the normal incident plane wave is coupled to vertical free-space radiation continuum to form triple Fano resonance with higher Q factor when the symmetry is broken. Numerical simulation is used to explore the influences of x-polarized and y-polarized plane wave on the above Fano resonances, and the results show that the Fano resonance of double degenerate resonance is polarization independent, while the non-degenerate resonance is polarization dependent. The findings in this work can provide an effective theoretical reference for designing other square lattice metasurface to realize the excitation and evolution of multiple Fano resonances.