Wave-based acoustic simulation methods are studied actively for predicting acoustical phenomena. Finite-difference timedomain (FDTD) method is one of the most popular methods owing to its straightforwardness of calculating an impulse response. In an FDTD simulation, an omnidirectional sound source is usually adopted, which is not realistic because the real sound sources often have specific directivities. However, there is very little research on imposing a directional sound source into FDTD methods. In this paper, a method of realizing a directional sound source in FDTD methods is proposed. It is formulated as an estimation problem of the initial value so that the estimated result corresponds to the desired directivity. The effectiveness of the proposed method is illustrated through some numerical experiments.