We approach the problem of an apparently random movement of small cytoplasmic vesicles and its relationship to centrosome functioning. Motion of small vesicles in the cytoplasm of BSC-1 cells was quantified using computer-assisted microscopy. The vesicles move across the cytoplasm frequently changing their directions with negligible net displacement. The autocorrelation function for consecutive velocities of individual vesicles becomes indistinguishable from zero in 10s. Variance in the displacement is proportional to time. The motion of vesicles is anisotropic: It has diffusivity along the radii drawn from the centrosome several times higher than the tangential diffusivity. This anisotropy is abolished by ultraviolet microbeam irradiation of the centrosome when the microtubule array loses radial structure. We conclude that the motion of the vesicles in the cytoplasm can be described as diffusion-like random walk with centrosome-dependent anisotropy. The present analysis quantitatively corroborates the 'trial and error' model of vesicular transport.