Light is an important vehicle for observing and obtaining image information about objects and is an important way of perceiving the environment. However, in the natural environment, there are often small particles or obstacles between the observer and the observed object that prevent direct imaging of the observed object. When there is a scattering medium in the imaging optical path, photons are scattered with the scattering medium and the incident wavefront of the light is destroyed, resulting in a change in the direction of light propagation, and the photoelectric imaging system does not work properly under these conditions. To solve the problem of not being able to image the observed object clearly in the presence of the scattering medium, in this paper, statistical averaging and lensless Fourier transform digital holography are used to achieve imaging through the scattering medium. The speckle is averaged through the rotating scattering medium, and the exposure time of the camera is increased so that the time average of the scattering field replaces the collective average, thus eliminating the effect of the random phase introduced by the scattering medium on the imaging process. This method of digital holography using statistical averaging and lensless Fourier transform has the advantages of simple and compact optical path structure, fast reconstruction speed, and low cost. Compared to wavefront shaping technology, transmission matrix technology, adaptive optics technology, and other methods of imaging through scattering media, this method does not require phase correction and complex image processing, target scanning, wavefront shaping, and other complicated operations.The experiments firstly investigate the effects of ground glass rotation speed and CCD exposure time on the peak signal-to-noise ratio of reconstructed images. The experiments show that different rotation speeds require different exposure times to achieve the highest peak signal-to-noise ratio, and the faster the rotation speed, the shorter the time required to reach the highest peak signal-to-noise ratio. The highest peak signal-to-noise ratio of 21.44 dB was obtained for the four sets of data at a rotation speed of 1.5 r/min and an exposure time of 800 ms. After obtaining the optimal experimental conditions, the imaging experiment through a single scattering medium was carried out. The laser light is divided into two beams by the beam splitter, one beam of light irradiates the object for transmission or reflection and then passes through the rotating ground glass as the object light, and the other beam is reflected by the mirror. After the incident on the convex lens, the convex lens converts the light beam from a plane wave to a spherical wave emitted by a point light source, to meet the conditions of lensless Fourier transform digital holographic recording. Then the reference light and the object light interfere after being combined by the beam combiner, and finally, the interference speckle image is recorded by the CCD. The experiments show that the method can reconstruct the object information for both transmissive resolution plates and reflective dolls and coins. On this basis, to solve the problem that actual imaging scenes rarely have a scattering medium with rotation or small displacement, we extend the application scenario of the method by introducing a stationary scattering medium. Experiments are carried out by loading a random speckle image on a spatial light modulator to simulate a stationary scattering medium. The experiments show that although the imaging quality is reduced compared to that through a single rotating scattering medium, the method is still able to image the target object clearly and achieve imaging through a double scattering medium. Finally, the reconstructed image is subjected to Butterworth high-pass filtering, and the contrast of the reconstructed image is effectively improved after the filtering.