Summary Reservoir parameter inversion is an essential geophysical method to quantify the reservoir volume. Oil-gas reservoirs are often presented as two-phase medium and anisotropic features, which lead to a great challenge for the reservoir parameters prediction. In the abstract, a new joint porosity and permeability inversion technology is proposed for 3D twophase cracked orthorhombic media based on the BISQ mechanism. First, we derive the porous elastic wave equation of 3-D two-phase orthotropic anisotropic medium and build the relationships among porosity, permeability and phase velocity. Then using the genetic algorithm, we conduct the porosity and permeability inversion with single-azimuth velocity dispersion by genetic algorithms, and analyse the influences that the different azimuths velocity dispersion have on the inversion accuracy. Finally, we implement the joint inversion of the porosity and permeability with multi-azimuths velocity dispersion, which makes use of advantages of the different azimuth, and analyze the algorithm stabilization and accuracy.