The path-integral techniques are used to study the problem of turbulent diffusion. A path-integral representation for the effective diffusion function of a passive scalar field is derived and the long-time effective diffusivity in Gaussian turbulence in the near-Markovian limit is calculated. The results confirm the negative effect of vorticity predicted by previous discussions. They also demonstrated that the helicity of the turbulence when present may be as important an influence as the vorticity. This paper has shown that the path-integral technique can be a useful way of approaching the problem of turbulent diffusion.