Since gaze estimation plays a crucial role in recognizing human intentions, it has been researched for a long time, and its accuracy is ever increasing. However, due to the wide variation in eye shapes and focusing abilities between the individuals, accuracies of most algorithms vary depending on each person in the test group, especially when the initial calibration is not well performed. To alleviate the user-dependency, we attempt to derive features that are general for most people and use them as the input to a deep network instead of using the images as the input. Specifically, we use the pupil shape as the core feature because it is directly related to the 3D eyeball rotation, and thus the gaze direction. While existing deep learning methods learn the gaze point by extracting various features from the image, we focus on the mapping function from the eyeball rotation to the gaze point by using the pupil shape as the input. It is shown that the accuracy of gaze point estimation also becomes robust for the uncalibrated points by following the characteristics of the mapping function. Also, our gaze network learns the gaze difference to facilitate the re-calibration process to fix the calibration-drift problem that typically occurs with glass-type or head-mount devices.