Catalyst warm-up control method for internal combustion engine, and catalyst warm-up control device

An internal combustion engine is mounted for power generation in a series hybrid vehicle and has an exhaust system with an upstream-side catalytic converter and a downstream-side catalytic converter. After starting of the internal combustion engine, the operation of the internal combustion engine is continued, without stopping the internal combustion engine even when the power generation request ceases, until completion of the warm-up of both of the upstream-side catalytic converter and the downstream-side catalytic converter. The internal combustion engine is operated with ignition timing retardation during a first period from the starting of the internal combustion engine to the completion of the warm-up of the upstream-side catalytic converter. During a second period from the completion of the warm-up of the upstream-side catalytic converter to the completion of the warm-up of the downstream-side catalytic converter, the internal combustion engine is operated without ignition timing retardation.