Speckle correlation imaging (SCI) has been considered one of the most promising techniques for computational imaging through a scattering medium. However, the image quality is not always acceptable in conventional SCI, especially when a complex object is involved. In this work, a modified phase retrieval algorithm is introduced to significantly improve the imaging quality of SCI. In the proposed scheme, nonzero-pixel constraints, rather than the real and nonnegative constraints, are employed as the object domain constraints of the iterative algorithm in the image reconstruction process. Experimental results are presented to show the performance enhancement of this scheme, inclusive of less iterations, better image quality, and higher reliability, in comparison with the conventional SCI method.