Livestock-associated methicillin resistant Staphylococcus aureus (LA-MRSA) colonizes livestock animals worldwide, especially pigs and calves. Although frequently carried asymptomatically, LA-MRSA can cause severe infections in humans. It is therefore important to better understand LA-MRSA spreading dynamics within pig farms and over pig movement networks, and to compare different strategies of control and surveillance. For this purpose, we propose a stochastic meta-population model of LA-MRSA spread along the French pig movement network (n = 10,542 farms), combining within- and between-farm dynamics, based on detailed data on breeding practices and pig movements between holdings. We calibrate the model using French epidemiological data. We then identify farm-level factors associated with the spreading potential of LA-MRSA in the network. We also show that, assuming control measures applied in a limited (n = 100) number of farms, targeting farms depending on their centrality in the network is the only way to significantly reduce LA-MRSA global prevalence. Finally, we investigate the scenario of emergence of a new LA-MRSA strain, and find that the farms with the highest indegree would be the best sentinels for a targeted surveillance of such a strain’s introduction.