Volumetric display technique has a great advantage of displaying realistic three-dimensional contents with a 360-degree viewing angle. However, most volumetric displays cannot provide mixed reality because their screens inside the displays obstruct the external scene. We design a 360-degree mixed-reality volumetric display using an asymmetric diffusive holographic optical element (ADHOE). The ADHOE has wavelength selectivity, and it diffuses the light with the only specific wavelength for the virtual object, so it is possible to optically combine the virtual object and the real scene. Also, the ADHOE has different vertical and horizontal diffusing angles, and it is suitable for a horizontal-parallax-only application. In our system, the parallax images are generated by the DMD, and they are projected sequentially on the ADHOE. The ADHOE is shaped as a slanted curved surface with respect to the optical axis, and some annoying color dispersion is observed due to the mismatch between the diffraction peak points of two different wavelengths. In order to solve this problem, the carrier frequency is applied to green elemental images and the proper Fourier filter cuts off the unwanted diffraction peak points. The Fourier transform with 2f optics is built to record the ADHOE where the angular spectral bandwidth is determined by adjusting the width of the incident object light. A 360-degree see-through display with ADHOE is implemented and the feasibility of mixed reality is verified successfully.