For the purpose of underwater detection and acoustic countermeasures，active sonar equipment is usually installed in the bow compartment of ships，and the sonar-emitting acoustic waves are propagated outward through the transmissive windows. Therefore，the research on the sound transmission properties of transmissive windows is of great practical significance. In order to solve the practical problem that it is difficult to calculate the sound transmission performance of the transmissive window，a hybrid analytical-numerical method is proposed for fast prediction of the insertion loss of the transmissive window. Firstly，the spherical harmonic expansion method and the superposition principle are utilized to calculate the sound field of the array piston source and then to obtain the sound pressure and normal vibration velocity caused by the source excitation. Secondly，the method of re-radiation， included in the Kirchhoff-Helmholtz module of COMSOL，is invoked to solve the insertion loss. Finally，a two-dimensional transmissive window model is established，and its all-round insertion loss is calculated by the method of this paper and the pure finite element method，respectively，to verify the accuracy and effectiveness of the method.
