Abstract: There is a class of slow wave propagation in bio-system and life phenomena with some new features which cannot be described by traditional wave theory based on the elastodynamics or fluid dynamics. To give a description on the new wave phenomenon, we suggest a new physical-mathematical model, which leads to a new dispersion relation k=1/2 ω/D, where k the wave number, ω the circular frequency (or angular frequency), D the diffusion coefficient in the relevant diffusion equation. This relation is quite different from those classical dispersion relations based on the elastodynamics or fluid dynamics. The present result couples wave propagation and diffusion—these are two different kinds of motions. From the relation the wave speed is derived as U=4kD=8πD/λ, which shows that wave speed depends not only upon the quantities describing wave (e.g. wave length λ) but also diffusion coefficient D. The theoretical prediction based the formula is in good agreement to that of experimental measurement.