A burner combustion method is employed in which at least two burners (2) are disposed opposite each other in a furnace (1) so as to cause combustion, the method comprising: cyclically changing at least one of a flow rate of a fuel fluid and a flow rate of an oxidant fluid supplied to the respective burners (2) while cyclically changing a concentration of oxygen in the oxidant fluid thereby cyclically changing an oxygen ratio obtained by dividing a supply oxygen amount by a theoretically required oxygen amount, whereby, the burners (2) are made to cause combustion in a cyclical oscillation state, wherein with respect to the cyclical change in an oscillation state of the burners (2), a phase difference is provided between a cyclical change in an oscillation state of at least one burner (2) and cyclical changes in oscillation states of other burners (2).