Various notifications on a display for e-mail arrival, micro-blog updates, and application updates are becoming increasingly important. Thus many studies have been done to make notifications not to prevent a user to achieve a task. In this paper, we propose a novel notification method, the peripheral notification that uses the human cognitive property, visual field narrowing, that a human does not recognize subtle changes in a peripheral visual field when he/she concentrates on a task and that he/she automatically recognizes the changes when not concentrating on the task. By only setting a notification icon in the area of visual field narrowing, a user automatically and easily accepts the notification only when his/her concentration breaks. We conducted two experiments to investigate a visual field narrowing region in a controlled environment and evaluate the effectiveness of peripheral notifications by comparing with a traditional method in a more realistic environment. As a result, we confirmed the visual field narrowing in a display, and our peripheral notification had advantages.