This paper presents a spectral element based numerical method for calculating the vibro-acoustic response of sandwich plates with adhesively-bonded corrugated cores. The study is motivated by the need of optimal designs for improving the structural-acoustic performance of the considered structures. A two-dimensional plate model is firstly developed based on the spectral element method (SEM) for obtaining the frequency-domain vibration response of the whole structure subject to incident harmonic acoustic wave. Thereafter the Rayleigh integral formula is used to calculate the transmitted sound power via its structure-borne path. Comparing with the conventional finite element method, the SEM, since it is formulated in the frequency domain by using the exact wave solutions for the governing differential equation, provides exact frequency-domain solutions meanwhile using much fewer number of degrees-of-freedom. This is proven by the numerical results of structural vibration response. Furthermore, parametric studies are performed to investigate the influence of the inclined angle of bonded corrugated core and the thickness of face plates on the transmitted sound power of sandwich plates under restriction of same area mass density. Although these design parameters have different effects on the sound transmission loss in different frequency-bands of interest, the impacts of both of them become more evident with the increase of targeted sound-insulating frequency.