This paper investigated driver glances in order to establish a method for inferring lane-change intent when a driver was performing a cognitively distracting task. A driving simulator experiment was conducted for collecting driver glances' data under a single-task (changing lanes) condition as well as a dual-task (the changing lanes and performing a secondary cognitive task) condition. The degraded detecting ability was shown on the intent inference under the dual-task condition. Comparisons of the glances' data between the two driving conditions revealed that the insufficient glances of looking at the side-view mirror and the delayed lane-change intent might cause the decrease of the detection rate. To establish an appropriate method to infer the lane-change intent for supporting a driver under such distracted conditions, we investigated the lane-change intent under different conditions, and the result showed the necessity of adjusting the inference algorithm for responding a driver who might be distracted by a non-driving cognitive task. This finding indicated that it was important to infer the correct driver intent for establish a support function system for avoiding a lane-change crash due to driver distraction.