Ignition conditions of homogeneous charge compression ignition engine operated on Dimethyl Ether were investigated with focus on temperature and pressure at ignition. The compression ignition of Dimethyl Ether has two stages of combustion, which were known as cool and hot flame respectively. The ignition conditions of both stages have significant effect on the control of a HCCI engine. In this paper, the ignition conditions of cool flame were examined for two modified single-cylinder engines of different compression ratio (ε=8.1 and 18.0 respectively) to clarify the effect of compression history on ignition temperatures. Chemical kinetic computation was also performed to confirm the findings from experiment. The ignition temperature of cool flame was definitely dependent on engine speed and compression ratio, and therefore the ignition conditions of both stages of combustion should not be regarded as unique like the use of a specific temperature in the criterion of ignition in a homogeneous computation.