We propose a new Tone Mapping Operator dedicated to the visualization of 360° High Dynamic Range images on Head-Mounted Displays. Previous work around this topic has shown that the existing Tone Mapping Operators for classic 2D images are not adapted to 360° High Dynamic Range images. Consequently, several dedicated operators have been proposed. Instead of operating on the entire 360° image, they only consider the part of the image currently viewed by the user. Tone mapping a part of the 360° image is less challenging as it does not preserve globally the dynamic range of the luminance of the scene. To cope with this problem, we propose a novel Tone Mapping Operator which takes advantage of 1) a view-dependant tone mapping that enhances the contrast, and 2) a Tone Mapping Operator applied to the entire 360 • image that preserves the global coherency. Furthermore, the proposed Tone Mapping Operator is adapted to the human eye perception of the luminance on Head-Mounted Displays. We present two subjective studies to model the lightness perception on such Head-Mounted Displays.