Holographic display is an ideal technology for near-eye display to realize virtual and augmented reality applications, because it can provide all depth perception cues. However, depth performance is sacrificed by exiting computer-generated hologram (CGH) methods for real-time calculation. In this paper, volume representation and improved ray tracing algorithm are proposed for real-time CGH generation with enhanced depth performance. Using the single fast Fourier transform (S-FFT) method, the volume representation enables a low calculation burden and is efficient for Graphics Processing Unit (GPU) to implement diffraction calculation. The improved ray tracing algorithm accounts for accurate depth cues in complex 3D scenes with reflection and refraction, which is represented by adding extra shapes in the volume. Numerical evaluation is used to verify the depth precision. And experiments show that the proposed method can provide a real-time interactive holographic display with accurate depth precision and a large depth range. CGH of a 3D scene with 256 depth values is calculated at 30fps, and the depth range can be hundreds of millimeters. Depth cues of reflection and refraction images can also be reconstructed correctly. The proposed method significantly outperforms existing fast methods by achieving a more realistic 3D holographic display with ideal depth performance and real-time calculation at the same time.