We propose a multi-hole periodic silver film array structure and explore the optical properties of the proposed structure using the finite-difference time-domain method. Simulation results reveal that when linearly polarized light is incident on the metal surface, the structure possesses extraordinary optical transmission due to the excitation of the surface plasmon polaritons and localized surface plasmon resonances. In view of this phenomenon, the optical transmission property of the proposed structure is further optimized by the angle between the central hole and side holes, polarization angle of the incident light, and structural parameters (i.e., diameters of the central hole and side holes, structural thickness, space between side holes and central hole). Further analysis of the variation of the transmission peak under different refractive indices shows that the structure has a high sensitivity to the refractive index of the surrounding environment. Thus, the proposed structure has potential applications in surface plasma filters and refractive index sensors.