A national screening in 2016 identified 88% of Danish pig herds positive for livestock-associated Methicillin-resistant Staphylococcus aureus (LA-MRSA). This highlights the importance of evaluating potential control measures that could reduce the prevalence of LA-MRSA among Danish pig herds. In addition to describing the effects of (1) reduced within-herd transmission, (2) increased biosecurity, and (3) movement restrictions, the eradication of LA-MRSA as a potential control measure was investigated using a simulation model mimicking the spread of LA-MRSA among pig herds between 2006 and 2015. The latter strategy was simulated either as eradication of a random selection of herds for surveillance or as a risk-based selection of herds based on their potential to spread LA-MRSA via pig movements in four different scenarios: low- vs. high-prevalence scenarios with control measures starting in 2007 and in 2010. Almost all control measures showed the potential to reduce the spread of LA-MRSA among pig herds, especially when implemented intensively and when control measures were combined. Risk-based selection of herds for eradication led to a greater relative reduction compared to random selection. In the high-prevalence scenario in particular, combinations including risk-based eradication led to the greatest relative reduction.