An apparatus for supplying a respiratory gas includes a conveyor device for conveying the respiratory gas, a conduit for feeding the respiratory gas conveyed by the conveyor device to a person, and a humidification device for humidifying the respiratory gas. A sensor device is configured to generate a signal indicative of the respiratory gas humidity and a control device is configured to control the humidification device with regard to the signal which is generated by the sensor device. A method of supplying a respiratory gas to a patient, in which the respiratory gas is introduced by means of a conveyor device into the conduit leading to the patient and is humidified, includes operating the conveyor device so that a respiratory gas pressure which is above ambient pressure is provided in the conduit, and adjusting the humidity on the basis of signals indicative of the relative and/or absolute humidity of the respiratory gas generated by the sensor device.