Ultrasound Nakagami imaging is an attractive method for visualizing changes in envelope statistics. Window-modulated compounding (WMC) Nakagami imaging was reported to improve image smoothness. The sliding window technique is typically used for constructing ultrasound parametric and Nakagami images. Using a large window overlap ratio may improve the WMC Nakagami image resolution but reduces computational efficiency. Therefore, the objectives of this study include: (i) exploring the effects of the window overlap ratio on the resolution and smoothness of WMC Nakagami images; (ii) proposing a fast algorithm that is based on the convolution operator (FACO) to accelerate WMC Nakagami imaging. Computer simulations and preliminary clinical tests on liver fibrosis samples (n = 48) were performed to validate the FACO-based WMC Nakagami imaging. The results demonstrated that the width of the autocorrelation function and the parameter distribution of the WMC Nakagami image reduce with the increase in the window overlap ratio. One-pixel shifting (i.e., sliding the window on the image data in steps of one pixel for parametric imaging) as the maximum overlap ratio significantly improves the WMC Nakagami image quality. Concurrently, the proposed FACO method combined with a computational platform that optimizes the matrix computation can accelerate WMC Nakagami imaging, allowing the detection of liver fibrosis-induced changes in envelope statistics. FACO-accelerated WMC Nakagami imaging is a new-generation Nakagami imaging technique with an improved image quality and fast computation.