We address an optical imaging method that allows imaging, which owing to the “memory-effect” for speckle correlations, through highly scattering turbid media with “Error Reduction - Hybid Input Ouput (ER-HIO)” algorithm. When light propagates through the opaque materials, such as white paint, paper or biological tissues, it will be scattered away due to the inhomogeneity of the refractive index. Multiple scattering of light in highly scattering media forms speckle field, which will greatly reduce the imaging depth and degrade the imaging quality. Some methods have been developed to solve this problem in recent years, including wavefront modulation method (WMM), transmission matrix method (TMM) and speckle correlations method (SCM). A novel approach is proposed to image through a highly scattering turbid medium, which combines speckle correlations method (SCM) with phase retrieval algorithm (PRA). Here, we show that, owing to the “optical memory effect” for speckle correlations, a single frame image of the speckle field, captured with a high performance detector, encodes sufficient information to image through highly scattering turbid media. Theoretical and experimental results show that, neither the light source, nor wave-front shaping is required in this method, and that the imaging can be easily realized here using just a simple optical system with the help of optical memory effect. Our method does not require coherent light source, which can be achieved with LED illumination, unlike previous approaches, and therefore is potentially suitable for more and more areas. Consequently, it will be beneficial to achieve imaging in currently inaccessible scenarios.