An apnea preventing stimulation apparatus having a conductive unit is attached to a mental region of a patient and electric pulses flow from the conductive unit to the mental region of the patient to thereby apply stimuli thereto. A formula is utilized to increase a rate of an output level of the amplitude in an electric pulse until a first time width elapses. Consequently, immediately after outputting stimulation signals, the amplitude of the electric pulse groups does not abruptly increase, thus enabling the patient to be hardly affected by the stimulation signals. Until just before the time reaches the end of a time width after the output start of the stimulation signal, the rate of the output level of the amplitude in the electric pulse groups does not reach 1, permitting the emotional strain on the patient to be eased.