Auditory alarm deafness is a failure to notice a salient auditory signal in a high-load context, which is one of the major causes of flight accidents. Therefore, it is of great practical significance for aviation safety to explore ways to avoid auditory alarm deafness under a high-load scenario. One potential reason for its occurrence could be the fact that cognitive resources are limited. Working memory (WM) capacity is important for the availability of cognitive resources. The present study investigated the effects of different types of WM ability and transcranial direct current stimulation (tDCS) combined with WM training on auditory alarm sensitivity in a simulated high-load aeronautical decision-making task in two experiments, with participants who were not trained pilots. The results showed that different types of WM storage capacity did not predict auditory alarm deafness. However, individuals with high executive function of WM were more sensitive to the auditory alarm than those with low executive function. During WM training, tDCS over the right dorsolateral prefrontal cortex not only improved WM executive function but also improved auditory alarm sensitivity under high-load conditions. These findings suggest that the storage and executive function of WM have different roles in auditory alarm sensitivity. WM training based on brain stimulation technology can provide empirical evidence for the enhancement of auditory alarm alertness and cognitive function in the human-machine context.