Conventional gaze tracking systems are limited in cases where the user is wearing glasses because the glasses usually produce noise due to reflections caused by the gaze tracker's lights. This makes it difficult to locate the pupil and the specular reflections (SRs) from the cornea of the user's eye. These difficulties increase the likelihood of gaze detection errors because the gaze position is estimated based on the location of the pupil center and the positions of the corneal SRs. In order to overcome these problems, we propose a new gaze tracking method that can be used by subjects who are wearing glasses. Our research is novel in the following four ways: first, we construct a new control device for the illuminator, which includes four illuminators that are positioned at the four corners of a monitor. Second, our system automatically determines whether a user is wearing glasses or not in the initial stage by counting the number of white pixels in an image that is captured using the low exposure setting on the camera. Third, if it is determined that the user is wearing glasses, the four illuminators are turned on and off sequentially in order to obtain an image that has a minimal amount of noise due to reflections from the glasses. As a result, it is possible to avoid the reflections and accurately locate the pupil center and the positions of the four corneal SRs. Fourth, by turning off one of the four illuminators, only three corneal SRs exist in the captured image. Since the proposed gaze detection method requires four corneal SRs for calculating the gaze position, the unseen SR position is estimated based on the parallelogram shape that is defined by the three SR positions and the gaze position is calculated. Experimental results showed that the average gaze detection error with 20 persons was about 0.70° and the processing time is 63.72 ms per each frame.