Digital micromirror devices (DMDs), owing to their rapid refresh rates, are among the most commonly used spatial light modulators in holographic three-dimensional near-eye displays. However, the modulation of DMD is typically confined to binary amplitude modulation, resulting in a noticeable presence of zero-order and conjugate noise, which significantly occupies the spatial bandwidth of the display optics and reduces the quality of optical reconstruction. To address these issues, we propose a computational framework of generating optimized binary computer-generated holograms for DMD-based holographic near-eye displays. Our work employs an iterative-based optimization strategy within a band-limited diffraction computation, thereby enhancing the display quality while achieving a considerable field of view by eliminating zero-order and conjugate noise. The proposed method is verified experimentally by displaying true three-dimensional images with low speckle noise and high contrast, opening a path towards next-generation of virtual reality/augmented reality display devices.