Statistical characteristics of double scattering speckle field in longitudinal motion is studied in detail. Its autocorrelation function of amplitude and intensity fluctuations are derived. At the receiving plane within the far-field diffraction region, the autocorrelation function of speckle intensity fluctuations is not generally statistically stationary. While, the time-varying speckle intensity variations become statistically stationary in the vicinity of the center of far-field diffraction plane. The velocity of the diffuser is in inverse proportion to the correlation time. The theoretical result is consistent with the experimental result.