Rock pores often contain two-phase or multi-phase fluids, so it is important to understand how the wave-induced fluid pressure diffusion affects dispersion and attenuation of elastic waves for resource exploration. To describe the propagation of elastic wave in a double-porosity medium saturated by two-phase fluids, a wave propagation model, including both global and local flow mechanisms and considering the effect of capillary pressure, is derived. The dispersion and attenuation characteristics of three longitudinal waves (P1, P2, P3) and one transverse wave (S wave) are investigated by analyzing a plane wave, and the effects of physical parameters, such as inclusion radius, water saturation, permeability and porosity, on the propagation characteristics of P1 wave are investigated. Theoretical analysis shows that the model derived in this work can be degenerated into the Biot model under specific conditions. According to the numerical simulation results, due to the coupling of global flow and local flow, the P1 wave velocity may decrease below the Gassmann-Wood limit. The physical explanation of this phenomenon is as follows: when considering the effect of capillary pressure, the coupling effect of global flow and local flow will break the basic assumption that rock is undrained. The relationship between physical parameters of porous medium and the dispersion and attenuation characteristics of elastic wave is complicated and nonlinear. Compared with Santos model, elastic modulus predicted by Santos-Rayleigh model is in good agreement with the experimental data in the low frequency band, which proves that this model has good reliability in modeling the velocity field of seismic exploration.