We investigate the dynamic properties of Brownian particle subject to a metastable periodic potential. By employing the Fokker-Planck equation, which we solve numerically by the matrix continued fraction method, we have calculated the full width at half-maximum (FWHM) λ(q) of the quasi-elastic peak of the dynamic structure factor, for large range of values of the wave-vectors q and for different temperature. Our results show that at low temperature and for different values of the ratio of the barriers ∆=V₂/V₁ the diffusion process can be described by a simple jump motion with the jump length equal to a/2 for ∆=1 and equal a for 0≤∆≤1/2. While for the other cases, the diffusion process consists of a superposition of both of them. At high temperature, the Fokker-Planck equation describes a diffusion process, which has some characteristic of jump and liquid-like regimes.