A method of controlling a power transmission system for a vehicle includes resuming fuel supply from a fuel cut condition during transition from an accelerator-off mode to an accelerator-on mode, setting a speed change inhibition time period of a continuously variable transmission (''CVT'') in correspondence to a speed change ratio, determining combustion attainment of an engine, and permitting variation of the speed change ratio of the CVT in accordance with the speed change inhibition time period and the determination of combustion attainment.