To appropriately start an engine which can respond to a variety of sorts of fuel.

A control device includes: a compression ratio variable mechanism 96 which can vary a compression ratio; a heat generating means 94 heating the inside of a combustion chamber 20; a fuel property measuring device measuring ignition performance of fuel; and an operation control device controlling operation of the compression ratio variable mechanism 96 and operation of the heat generating means 94 based on the ignition performance of the fuel measured by the fuel property measuring device, in start of an internal combustion engine. The operation of the compression ratio variable mechanism is controlled to make the compression ratio higher as the ignition performance of the fuel gets lower, and the operation of the heat generating means is controlled to make a heating time longer as the ignition performance of the fuel gets lower.