A wick operating structure of the lever actuation type for an oil burner capable of finely adjusting the combustion with high accuracy during the combustion operation. The structure includes an operation lever for rotating a wick operating shaft which is provided with a drive pin and a plurality of drive levers pivotally moved independent from one another so as to be accessible to the drive pin. The drive levers are formed with a V-shaped recesses which are different in configuration from one another little by little and in which the drive pin is alternatively fitted to cause the operation lever to be pivotally moved to different positions little by little.