Anaerobic digestion (AD) is an efficient way to treat municipal organic waste and generate renewable energy, therefore, it is gaining increasing attention in research and engineering application. While one of the most important metabolic intermediates connecting acidogenesis and methanogenesis is acetate, the study of microbial consortia and functional microorganisms’ dynamics involved in acetic acid feeding AD system may help adjusting AD performance and maintaining a stable methane production. In this study, a laboratory-scale anaerobic digester was constructed to operate AD system feeding acetic acid as the sole substrate. The acetic acid volumetric loading rate (VLR) was lifted from 0.2 to 5.0 g/(L·d) sequentially according to the experimental stages (totally 22 acetic acid VLR stages). According to the volumetric biogas production (VBP), the process was divided into four phases: acclimation phase (VLR 0–0.8 g/(L·d)), lifting phase (VLR 1.0–2.7 g/(L·d)), stable phase (VLR 3.0–4.4 g/(L·d)), and recovery phase (VLR 4.4–5.0 g/(L·d)). Three VFAs shocks occurred in the beginning of lifting phase, stable phase, and recovery phase, respectively. Combined 16S rRNA high-throughput sequencing and binning assembled through metagenomic sequencing, it was revealed that Methanosarcina was the main genus consuming acetate during the first VFAs shock. Syntrophic acetate/butyrate-oxidizing bacteria (Synergistaceae, Spirochaetaceae, Cloacimonas, DMER64) were enriched in the second VFAs shock, which were interacted with hydrogenotrophic methanogen Methanosarcina mazei. Furthermore, acetoclastic methanogen Methanosaeta and a novel propionate-oxidizing bacteria Petrimonas were highly abundant after the third VFAs shock. The redundancy of functional microorganisms and metabolic pathways helped the system relieving acid inhibition.