1. A start system for an internal combustion engine of a hybrid vehicle, the hybrid vehicle including an internal combustion engine, a differential mechanism, and a transmission gear mechanism, the internal combustion engine being connected to the differential mechanism, the transmission gear mechanism being provided in a power transmission path between the differential mechanism and driving wheels, the transmission gear mechanism being configured to be able to select one of a plurality of gear positions, the hybrid vehicle being configured to use at least one of the differential mechanism and the transmission gear mechanism to temporarily change an engine speed in starting of the internal combustion engine, the start system comprising: an electronic control unit configured to determine a duration for which the engine speed needs to be changed in starting of the internal combustion engine, the electronic control unit being configured to determine a degree of change in the engine speed in starting of the internal combustion engine, and the electronic control unit being configured to determine whether the engine speed needs to be changed by changing the gear position of the transmission gear mechanism based on the degree and the duration.