Much research in optics was conducted to retrieve phase of the light field, e.g., via a reference wave (such as holography) or single-path optical diffraction. However, it is well recognized that a complete application of complex-field imaging (i.e., amplitude and phase) is still restricted by the existence of scattering media. In this Letter, we report high-resolution complex-field imaging with single-pixel detection, which can effectively suppress scattering effect. Complex fields are retrieved by using a series of collected single-pixel light intensities with an alternating projection (AP) method. A momentum and the denoising engine are integrated into the iterative process to increase convergence speed and reduce sampling ratios with quality enhancement of the retrieved complex fields. A series of optical experiments are designed and conducted, and it is experimentally demonstrated that the retrieved complex fields related to the object are of high quality. The proposed method could open an avenue for a wide range of applications related to complex-field imaging through scattering media.