The volume exploration refers to the observation of internal structures by manipulating visualization widgets such as a slicing plane. Since the advent of a commercial holographic display, the demand for 3D contents is also increasing in the medical visualization area. Holographic displays deliver a set of viewpoints through the lenticular lens so that a user can observe different sides of the object without wearing a pair of special glasses. Moreover, it comes natural for the user to perform the volume exploration using mid-air interaction. In this work, we present a novel volume exploration technique for holographic display. To accelerate the hologram rendering, we adopt the volume rendering pipeline to the holographic display mechanism. Also, to support a spatial interaction for volume exploration, we develop a cut-and-annotate interaction between volume object and point cloud. The proposed voxel classification algorithm produces a set of class properties for delineating different structures of the 3D object. We demonstrate our volume exploration method on several volume data sets under real-time user interaction.