Because of the special structure and intracellular functions of myosin Ⅵ molecular motor, its dynamic principle has become a research focus. Starting from its structure and experimental phenomenon, the elastic-diffusion model of myosin Ⅵ in a periodic potential field is established, and the stochastic dynamics of the molecular motors, which conform to the Langevin equation, is analyzed by Monte Carlo simulations. By means of the environmental noise, myosin Ⅵ molecular motors could take stable stepping motion and effective transport according to its elastic potential energy and periodic potential of track, and a load can weaken the transportation power of the molecular motor system. For a given elastic coefficient, the longer the elastic chain of myosin Ⅵ, the lower the average velocity of it. By selecting a reasonable size of elasticity coefficient, the average velocity can be the maximum for a given elastic chain. In addition, the load can increase exponentially the mean dwelling time of myosin Ⅵ at the connection site.