Much attention has been paid to the Brownian Motion summing up a class of physical phenomena. Recently，both computer simulations and experiments have shown that a “memory effect” is attached to the Brownian motion. A model for describing this effect has been constructed in this paper. The results of the calculations in steady case have shown that the second moment of the displacement fluctuation of micro particles is still proportional to the time intervals，and this effect eventually expresses the increase in fluid viscosity.