The authors already have proposed a novel method of HRIR customization for synthesizing stationary sounds in the median plane based on subjective tuning of three parameters at each static source position. For synthesizing both stationary and dynamic sounds, this study extends the previous study to customize spatially continuous HRIRs in the median plane. The median plane in the upper hemisphere was systematically divided into two sectors, and three parameters were tuned at three positions (0 degrees, 70 degrees, and 180 degrees), which are the endpoints of the two sectors, with listening to moving sounds synthesized by filtering the obtained spatially continuous HRIRs. Thus, the entire median-plane HRIRs in the upper hemisphere can be customized by subjective tuning of nine parameters only. Subjective localization listening tests were carried out to assess the customization performance using both stationary and moving sounds. When the stationary sounds were presented to nine subjects, the localization performance with the customized HRIRs was comparable to that with the individual HRIRs, but it was significantly better than that with the Kemar HRIRs. When the moving sounds were presented to four subjects, all subjects perceived the center position of the target trajectory more accurately with the customized HRIRs than with the Kemar HRIRs. The error with the customized HRIRs was comparable to that with the individual HRIRs. Therefore, it can be concluded that to make desired perception of both stationary and moving sounds is possible by the proposed customization methods.