Directivity of a sound source originates from the source’s shape and its size relative to wavelength. Therefore, the directivity varies with a frequency of a sound. In order to precisely simulate a directivity of a source in the finite-difference time-domain analysis, basically, it is necessary to model the shape of the source geometrically in detail. In the case of sources with complex shapes, however, geometrically precise modeling of the source shape requires small size of spatial discretization, and such a fine mesh discretization results in huge computational costs. In this study, applying a basic theory of Fourier analysis in which arbitrary directivity can be constructed by linear combination of spherical harmonic function, the condition of the sound source for the finite-difference time-domain method to reduce computational cost and to enable efficient analysis against a source with complex directivity characteristics is investigated. Spatial distribution of sound pressure of initial condition for respective spherical harmonic function and correction method of spectral characteristics for the finite-difference time-domain analysis are described.