A control apparatus for a power unit equipped with an internal combustion engine and outputs a power. The control apparatus according to the invention starts engine operation when the required power becomes equal to or larger than an engine start threshold during engine stop, and stops engine operation when the required power becomes equal to or smaller than an engine stop threshold during engine operation. The internal combustion engine is equipped with a catalyst. When the purification capacity of the catalyst is lower than a start threshold correction threshold, a value smaller than a reference engine start threshold is set as the engine start threshold. When the purification capacity of the catalyst is equal to or higher than the start threshold correction threshold, a value equal to the reference engine start threshold or a value larger than the reference engine start threshold is set as the engine start threshold.