A spark-ignition direct injection engine is provided. Within a CI combustion applying range with low engine load compared with a first load, at least hot EGR gas is introduced in a cylinder 18. On the other hand, in a high engine low part of a SI combustion applying range, the entire range except the full-load range, cooling EGR gas cooled through heat exchange is introduced into the cylinder 18. Within the low engine low part of the SI combustion applying range, hot EGR gas, in addition to cooling EGR gas, is introduced in the cylinder 18.