A deep neural network (DNN) is constructed to predict the magnitude responses of the head-related transfer functions (HRTFs) of users for a specific direction and a specific ear. Using the CIPIC HRTF database (including 25 azimuth angles and 50 elevation angles for both ears), we trained 2500 DNNs to predict magnitude responses of all HRTFs of a user. To reduce training time, we propose to use the final weights of the trained DNN of a nearby direction as the initial weights of the current DNN under training since magnitude responses of the HRTFs are smoothly changing across nearby directions. Analysis of variance (ANOVA) was performed to show that the proposed training scheme produces equivalent magnitude responses of HRTFs as the standard training scheme with random initial weights in terms of the log-spectral distortion (LSD) measure. Meanwhile, the proposed training scheme can dramatically reduce training time by more than 95%.