The sound power level is a physical quantity indispensable for evaluating the amount of sound energy radiated from electrical and mechanical apparatuses. The precise determination of the sound power level requires the qualification of the measurement environment, such as a hemi-anechoic room, by estimating the deviation of the sound pressure level from the inverse-square law. In this respect, Annex A of ISO 3745 specifies the procedure for room qualification and defines a tolerance limit for the directivity of the sound source, which is used for the qualification. However, it is impractical to prepare a special loudspeaker only for room qualification. Thus, we developed a simulation method to investigate the influence of the sound source directivity on the measured deviation of the sound pressure level from the inverse-square law by introducing a quantitative index for the influence of the directivity. In this study, type 4202 reference sound source by Brüel & Kjær was used as a directional sound source because it has been widely used as a reference standard for the measurement of sound power levels. We experimentally obtained the directivity of the sound source by measuring the sound pressure level over the measurement surface. Moreover, the proposed method was applied to the qualification of several hemi-anechoic rooms, and we discussed the availability of a directional sound source for the process. Analytical results showed that available reference sound sources may be used for the evaluation of hemi-anechoic rooms depending on the sound energy absorption coefficient of the inner wall, the directionality of the microphone traverse, and the size of the space to be qualified. In other words, the results revealed that a reference sound source that is once quantified by the proposed method can be used for qualifying hemi-anechoic rooms.