In this work we present a general theory for diffusion mechanism of Brownian particle submitted to a symmetric periodic triple-well potential. The kinetics description is done by the Fokker-Planck equation, which is resolved numerically using the Matrix Continued Fraction Method, in order to calculate some important correlation functions. The half-width lambda(q) at half maximum of the quasi-elastic peak of dynamic structure factor S(q, omega) and the diffusion coefficient D are studied in the high friction regime and low temperature for different form of triple-well potential. Our numerical results of half-width lambda(q), show that the diffusion process in triple-well potential can be described by a superposition of both simples hopping and liquid-like motion when the ratio Delta of two potential barriers V-1 and V-2 is less than one (Delta < 1) and by the longs jumps when Delta tends towards one. For some values of ratio of potential barriers, the diffusion coefficient results show that the intermediates potential barriers accelerate the diffusion process.