A control device for a hybrid vehicle includes a driving control part configured to acquire for each driving road section from a server a value of the output parameter linked with a vehicle speed of the same extent as the scheduled vehicle speed when driving over a driving road section on a scheduled driving route to calculate for each driving road section the scheduled vehicle demanded output when driving over the driving road section or acquire from the server the scheduled vehicle demanded output for each driving road section calculated based on the value of the output parameter for each driving road section at the server to heat the catalyst device before using the output of the internal combustion engine as part of the drive power when there is the driving road section where the scheduled vehicle demanded output becomes the engine start output or more.