The driver steering performance is strongly related to gaze behavior in natural driving. The investigation of gaze behavior is crucial for understanding driver response to driver-automation shared control, which was developed to reduce the workload of drivers while keeping them in the control loop. This study focused on driver gaze behavior and its relationship to the steering performance when driving with different levels of shared control. Shared control was achieved through a haptic guidance steering system, which provided active assistant torques on the steering wheel. A driving simulator experiment was conducted with 15 participants, who drove five trials, each with a different level of shared control: first, no haptic guidance, second, normal haptic guidance, third, strong haptic guidance, fourth, having a driver's hands hovering over the steering wheel as a standby during automated driving, and, fifth, having a driver's hands free for a long time during automated driving. The results show a tendency that the correlation between gaze and steering movements decreased when the automation authority of shared control increased. A reduction in the lead time of gaze over steering movement was found in the condition of strong haptic guidance compared to normal haptic guidance and manual driving. This study suggests the potential of using the relationship between gaze behavior and the steering performance to analyze driver interaction with automation.