In this paper, the sound field of a more general directional radiator in a stratified medium is treated, and the concept of directivity is applied to calculation of the normal modes. The result shows that the normal-mode field of a directional radiator can be obtained by supplementing the normal-mode expression of a omnidirectional point source with the directivity-excitation-function, which is dependent on the position and directivity of the radiator. In addition, the normal-mode fields of the radiators with vertical-symmetrical, vertical-antisymmetrical, single-side and sharp directivity are calculated, respectively.For the vertical line array in a homogeneous water-layer, if the source distribution is proportional to the eigenfunction of some normal mode, the zeros of the directivity-excitation-function are just corresponding to the directions of eigen-rays of other normal modes.