The growing demand of clean and efficient propulsion and energy systems has sparked an interest in understanding the low-temperature combustion at high-pressure. Cool flame extinction limits and flame structures at elevated pressure conditions provide insights of the low-temperature and high-pressure fuel reactivity. Moreover, pressure has a significant impact on cool flame chemistry. Dimethyl ether (DME) with strong low-temperature chemistry, has been chosen to study its non-premixed cool flame at high pressure. This paper investigates the effects of pressure on cool flame structure, extinction, and transition limits of DME experimentally and computationally. Both experimental data and numerical simulations show that the higher pressure has higher cool flame extinction strain rates. Furthermore, it is shown that the reignition transition from cool flame to hot flame also occur at higher strain rates with pressure. The detailed kinetic analyses have also been studied to show how pressure affects the chemistry of cool flames.