Linear depolarization ratios (LDR) characteristics of spheroid dust aerosol particles are studied based on discrete dipole approximation (DDA) for size parameters from 0.1 to 23 (corresponding to effective radius from 0.01 μm to 2 μm at wavelength of 0.55 μm). The effects of the particle asphericity degree on the LDRs characteristics for both monodisperse and polydisperse dust aerosols are performed by comparing LDRs characteristics at different spheroid aspect ratios. For monodisperse particles, the LDRs of spheroid dust aerosol have different behaviors as a function of scattering angle in the Rayleigh and Mie domains. In the Rayleigh domain, the LDRs are small with a value of 1%, in the forward- and backward-scattering directions with the scattering angles of 0° and 180°. While the LDRs show maxima of 100%, at side-scattering angles of 90°. In the Mie domain, the LDRs have no obvious extremum distribution, and reveal significantly enhanced backscattering values. The degree of asphericity of monodisperse dust particles generally increases their LDRs in the Rayleigh domain but not in the Mie domain. However, for polydisperse particles, the degree of dust asphericity increases with the LDRs except in the side-scattering regions (80°~100°) where the LDRs reach maxima.