Passive seismic source imaging can extract geophysical information from underground noise and has been widely utilized in geophysical research. Compared with conventional active seismic exploration, it is low-cost and eco-friendly; however, the application of passive seismic data is limited by coherent noise in the virtual-shot gathers. An approach involving direct denoising in the virtual-shot gathers has not previously been discussed; therefore, we present an iterative denoising strategy for passive seismic data. The reflection-preserving characteristic of focal transformation is adopted in the virtual-shot gathers to eliminate the coherent noise, and L1-norm sparse inversion is utilized to obtain a more accurate solution during focal transformation. A key aspect of this strategy is clean focal operator building at high noise levels. We apply local similarity as the criterion for extracting the majority of reflection energy for the focal operator. Because of strong coherent noise, a clean focal operator cannot be obtained in one iteration. We therefore obtain both denoised passive seismic data and a clean focal operator by denoising using a cleaner focal operator and operator building using updated denoising results. The presented approach can overcome the limits of coherent noise in virtual-shot gathers, which is significant for subsequent data processing and wider application. Synthetic examples achieve excellent performance in coherent noise attenuation and reflection energy reconstruction, especially in far-offset sections.