We discuss the superdiffusive motion of a random walk in a medium containing random velocity fields. For a two-dimensional layered medium with y-dependent random velocities in the x direction u(y), 〈(t)〉∼, with 2ν=3/2, and with strong sample-to-sample fluctuations. The probability distribution of displacements, averaged over environments, takes a non-Gaussian scaling form at large time, 〈P(x,t)〉∼f(x/), where v(u)∼exp(-) for u≫1, with δ=4/3. For an isotropic two-dimensional medium with (y)=f(y) and (x)=f(x), we find ν=2/3 and δ=1-ν=3.