INTRODUCTION: HIV prevalence is high among men who have sex with men (MSM) in Baltimore, Maryland, United States, and the levels of viral suppression among HIV-positive MSM are relatively low. The HIV Prevention Trials Network 078 trial seeks to increase the levels of viral suppression among US MSM by increasing the rates of diagnosis and linkage to care and treatment. We estimated the increases in viral suppression needed to reach different HIV incidence reduction targets, and the impact of meeting diagnosis and treatment targets. METHODS: We used a mathematical model of HIV transmission among MSM from Baltimore, US, parameterised with behavioural data and fitted to HIV prevalence and care continuum data for Baltimore wherever possible, to project increases in viral suppression needed to reduce the HIV incidence rate among Baltimore MSM by 10, 20, 30 or 50% after 2, 5 and 10 years. We also projected HIV incidence reductions achieved if US national targets - 90% of people living with HIV (PLHIV) know their HIV serostatus, 90% of those diagnosed are retained in HIV medical care and 80% of those diagnosed are virally suppressed - or UNAIDS 90-90-90 targets (90% of PLHIV know their status, 90% of those diagnosed receive antiretroviral therapy (ART), 90% of those receiving ART are virally suppressed) are each met by 2020. RESULTS: To reduce the HIV incidence rate by 20% and 50% after five years (compared with the base-case at the same time point), the proportion of all HIV-positive MSM who are virally suppressed must increase above 2015 levels by a median 13 percentage points (95% uncertainty interval 9 to 16 percentage points) from median 49% to 60%, and 27 percentage points (22 to 35) from 49% to 75% respectively. Meeting all three US or 90-90-90 UNAIDS targets results in a 48% (31% to 63%) and 51% (38% to 65%) HIV incidence rate reduction in 2020 respectively. CONCLUSIONS: Substantial improvements in levels of viral suppression will be needed to achieve significant incidence reductions among MSM in Baltimore, and to meet 2020 US and UNAIDS targets. Future modelling studies should additionally consider the impact of pre-exposure prophylaxis for MSM.