A near-field Head-Related Transfer Function (HRTF) data set measured on a KEMAR head and torso simulator with high distance resolution and multiple elevations is presented ('KEMAR_NFHRIRmea_1cm.sofa'). HRTFs are measured at 83448 spatial points at distances ranging from 20 to 110 cm, elevations from -25° to 35°, and azimuths from 0° to 355°. The distance resolution of the HRTF data is 1 cm, higher than that of any existing public near-field HRTF databases. Therefore, the dataset enables further exploration of the distance dependence of near-field HRTFs, and is beneficial for applications of realistic and dynamic binaural rendering of nearby sound sources. An additional data set of simulated HRTFs with 1.5 cm distance resolution is also provided ('KEMAR_NFHRIRsim_1.5cm.sofa') for a direct comparison with the measured HRTFs or other purposes.