Open or partially open boundary conditions in fully or partially saturated rocks possibly occur in many realistic geologic scenarios, and it is critical to understand the influences of wave-induced fluid pressure diffusion and anelasticity for many fields of earth science and engineering applications. Under the framework of Biot’s poroelasticity, by proposing a scale factor to represent the opening degree of the boundary, we have investigated the influences of boundary conditions on the seismic wave dispersion and attenuation in partially saturated rocks. It is found that there exist two types of fluid pressure diffusion taking place simultaneously: the mesoscopic fluid pressure diffusion between the two immiscible fluids (e.g., gas and brine) and the fluid flow associated with the outer boundary. The boundary conditions significantly control the seismic wave dispersion and attenuation signatures. The coupled fluid pressure diffusion of mesoscopic flow and outer boundary flow expedite the pore pressure equilibration processes and make the characteristic frequency one order of magnitude higher than the undrained scenario. The drained and partially drained conditions also significantly decrease the velocity of partially saturated rocks, which can be even lower than that of Gassmann’s prediction and dry rock. The reliability of the theoretical model also is validated by comparing it with the numerical simulation for drained and undrained conditions. We have determined that the proposed model is capable of better interpreting the logging data of velocity-saturation relationship for a partially saturated carbonate reservoir and experimental data of wave dispersion for a fully saturated sandstone, both of which are possibly exposed to the open boundary conditions.