A premixing apparatus that mixes a fuel gas with air and supplies an air-fuel mixture in a burner through a fan includes a control device that is configured to carry out a third control that: calculates and memorizes a lower limit of a rotational speed of a fan, at which an increase of an opening degree of a variable throttle valve becomes necessary, as a first threshold; and when the rotational speed of the fan increases to the first threshold or faster next time, immediately changes the opening degree of the variable throttle valve to an increased opening degree, which is larger than a predetermined standard opening degree and is obtained by multiplying a deviation of the rotational speed of the fan from the first threshold by a predetermined coefficient.