Voluntary medical male circumcision (VMMC) among men who have sex with men (MSM) may protect against HIV acquisition. We conducted a series of analyses to assess if expanded VMMC might reduce HIV incidence among MSM effectively and economically. We used a deterministic compartmental model to project new HIV cases (2016-2026) under annual VMMC coverage rates (λ) ranging from 0.0001 to 0.15. The 'number needed to avert' (NNA) is defined as the cumulative number of VMMCs conducted up to that year divided by the cumulative number of HIV cases averted in that specific year. Compared with the baseline circumcision coverage rate, we projected that new HIV cases would be reduced with increasing coverage. By 2026 (last year simulated), the model generated the lowest ratio (11.10) when the annual circumcision rate was the most optimistic (λ = 0.15). The breakeven point was observed at the year of 2019 with the annual VMMC coverage rate of 0.001. The total cost saved by averting HIV cases would range from 2.5 to 811 million US dollars by the end of 2026 with different hypothetical coverage rates. Our model suggests that acceleration in VMMC implementation among MSM could help stem the HIV/AIDS epidemic.