Marine heatwaves (MHWs), episodic periods of abnormally high sea surface temperature (SST), severely affect marine ecosystems. Large Marine Ecosystems (LMEs) cover ~22% of the global ocean but account for 95% of global fisheries catches. Yet how climate change affects MHWs over LMEs remains unknown, because such LMEs are confined to the coast where low-resolution climate models are known to have biases. Here, using a high-resolution Earth system model and applying a "future threshold" that considers MHWs as anomalous warming above the long-term mean warming of SSTs, we find that future intensity and annual days of MHWs over majority of the LMEs remain higher than in the present-day climate. Better resolution of ocean mesoscale eddies enables simulation of more realistic MHWs than low-resolution models. These increases in MHWs under global warming poses a serious threat to LMEs, even if resident organisms could adapt fully to the long-term mean warming.