This paper is concerned with the development of a theoretical model for the prediction of the sound radiated by serrated trailing-edges. The proposed model is based on Fourier expansion and Amiet's formulation. By using an iterative PDE-solving procedure, the scattered pressure field on the surface of an airfoil with sawtooth trailing-edge serrations is obtained. The far-field sound is then evaluated using the surface pressure integral based on the theories of Kirchhoff and Curle. The power spectral density (PSD) of the far- field sound is then related to the wavenumber spectral density of the hypothetical surface pressure under the turbulent boundary layer that would exist when the trailing-edge is absent. Numerical evaluation of the new model has shown better agreement than that obtained using Howe's model. Based on the new model, the sound reduction achieved by a trailing-edge with sharp sawtooth serrations is around 5-10 dB for a wide frequency range. This result agrees better with experiments, in which the average sound reduction is reported to be 5-7 dB. The results obtained using the new analytical model also agree well with FEM computations, suggesting that the model developed in this paper can capture the essential physics and give correct predictions for the sound generated by serrated trailing- edges. In the end, the physical mechanism of noise reduction is found to be the destructive interference effect of the scattered pressure field.