High dynamic range (HDR) display prototypes have been built and used for scientific studies for nearly a decade, and they are now on the verge of entering consumer market. However, problems exist regarding the accurate color reproduction capabilities on these displays. In this paper, we first characterize the color reproduction capability of a state-of-art HDR display through a set of measurements, and present a novel calibration method that takes into account the variation of the chrominance error over HDR display's wide luminance range. Our proposed 3D octree forest data structure for representing and querying the calibration function successfully addresses the challenges in calibrating HDR displays: (i) high computational complexity due to nonlinear chromatic distortions, and (ii) huge storage space demand for a look-up table (35GB vs 100kB). We show that our method achieves high color reproduction accuracy through both objective metrics and a controlled subjective study.