The attenuation and dispersion characteristics of seismic waves in fluid-saturated porous media are one of the key indicators for identifying hydrocarbon reservoirs. This study proposes an elastic wave propagation model for dual-phase HTI media by integrating Biot's dual-phase theory with HTI anisotropic medium theory, deriving a three-dimensional first-order velocity-stress equation, and constructing a 12th-order staggered-grid finite-difference algorithm with PML boundary conditions. Numerical experiments demonstrate that: The fluid-phase parameter (R) exhibits a significant positive correlation with the slow P-wave velocity, while its energy attenuation rate increases exponentially with higher R values. The solid-fluid coupling coefficients (Q₁/Q₃) show a linear regulatory relationship with the energy attenuation of fast/slow P-waves but have no significant impact on shear wave propagation characteristics. Simulations using the Marmousi complex model verify the numerical stability of the algorithm under strongly heterogeneous geological conditions.