The free random walk approach has been used to analyze the attenuation of the NMR signal due to spin dephasing in the presence of a constant and pulsed parabolic magnetic field. The spin echo sequence was chosen to examine the attenuation of the NMR signal resulting from self-diffusion. In the framework of the gaussian approach, the long-time limit calculations predict more pronounced diffusion weighting for the parabolic field than for linear magnetic field. Analytical results were obtained and compared with those from other approaches based on a variety of different of approximations.