The demand for near-field Head-Related Transfer Functions (HRTFs) has been growing during the last years due to an increasing interest in the plausibility of virtual auditory events. To avoid audible artifacts during binaural rendering and reproduction, near-field HRTF data on a dense spatial grid is desired, but the acquisition procedure is then time-consuming and prone to measurement error. Fast acquisition of HRTFs with a high azimuthal resolution has been enabled by continuous-azimuth measurements with the aid of LMS (Least Mean-Square)-type adaptive filtering, but existing near-field HRTF databases still only cover a few discrete source distances. In the studies presented in this paper, we developed and validated a novel measurement setup for continuous-distance acquisition of near-field HRTFs. We adapted the LMS algorithm to extract near-field HRTF data at any distance within the measurement range. We also evaluated the measurement accuracy by analyzing the estimation error from the adaptive filtering algorithm and the objective HRTF spectrum features.