This paper proposes a speed control method to move an autonomous mobile robot safely under the environment where blind areas exist. Sensors like a LRF or an optical camera cannot detect the areas in the backside of walls, pillars or objects. When a person suddenly appears from these blind areas, the mobile robot is very likely to collide with him/her, if its speed reduction performance is limited. In this paper the safety speed of robot is carefully controlled using the distance information between the robot and the blind areas as well as obstacles. Meanwhile, the optimum path is generated to minimize the cost of moving time, considering the lengthened time cost caused by speed control process. The effectiveness of the proposed method is confirmed by both the computer simulation and the experiment using a real robot.