A new head-related transfer function (HRTF) prediction method using tensor completion is proposed to estimate the HRTF in unmeasured directions based on sparse measurements and achieve high spatial resolution HRTF for individual subject. A three-order incomplete tensor prediction model is constructed to describe HRTF with a multi-dimensional structure depending on the subspaces of azimuth, elevation and frequency. Then, low rank tensor completion method is applied to complete this tensor by exploiting the hidden spatial structures of HRTF data, aiming to obtain the HRTF in unmeasured directions based on a small set of sparse measurements, in which gradient descent algorithm and line search strategy are used. Experiments have been conducted based on CIPIC HRTF database to evaluate the prediction performance. The objective results suggest that the proposed method has a better prediction performance than other tensor and linear interpolation methods. The subjective tests show that the proposed predicted HRTF is more approximate to the original one in sound localization similarity.