In a stream data processing method in which part of stream data is defined as a processing target and the time control information which indicates the advance of the time is inserted into the stream data, time information of the received stream data is stored in a next ignition time holding area as an ignition time. A processing module for generating the time control information at a time different from the time of reception of the stream data is extracted out of a query that indicates how the stream data is to be processed. Based on the extracted processing module and the time information indicating the time of the reception of the stream data, the ignition time is calculated and stored in the next ignition time holding area. The time generation module inserts the time control information at the ignition time held in the next ignition time holding area.