An optical switch based on polarization state control is designed by using a rectangular-like nanorods tetramer composed of four Au nanorods. The finite element method is used to study the response characteristics of the structure to incident light polarization. It is found that the transmission spectrum of the structure dependent strongly on the polarization direction of the incident light. When the polarization angle of the incident light changes by π/2, the switching ratio of the characteristic peaks can reach 27.81 dB and 21.65 dB, respectively. The analysis shows that the switching effect is mainly caused by the different near-field coupling strength between the horizontal double rod and the vertical double rod at the different polarization states. The relationship between the transmittance and the polarization angle of the structure obeys the Malus law. In addition, the influence of structural parameters on the response characteristics of optical switches is studied by changing the structural parameters of the rectangular-like nanorod array. On this basis, the influence of the periodic parameters on the transmission spectrum of the unit structure under the horizontal and vertical polarization of the incidence light is studied by changing the period parameters of the array. These results can provide a theoretical basis for the design of tunable dual-wavelength polarization-controlled optical switch.