In this paper the radiation property of the one-dimensional periodic leaky-wave structure is analysed using a new hybrid method, which involves the mode expansion method for expanding the periodic aperture field in terms of spatial harmonics and the method of effective radiation sections for transforming the expanded fields into far fields. Using this method, the radiation of each spatial harmonic can be achieved, and the contributions of the harmonics (especially the bounded modes) to the total radiation of the periodic leaky-wave structure can be calculated. The main findings in this paper demonstrate that the bounded modes in a finite length structure have obvious contribution to the far-field radiation, which was considered to be non-radiative and always ignored in the conventional researches.