For indoor security robots, face recognition is an important ability. However, face recognition is suffered from the limitation by environment uncertainties, the factors including perceptual aliasing, occlusion, illumination changes and significant viewpoint changes. These uncertainties will affect the recognition accuracy and processing time, which will cause the security concerns. This paper proposes a convolutional neural networks-based face recognition system for the mobile robots to perform visual perception and control tasks. The trained model proposed in this paper (i.e., FaceNet) is compared and tested against two different algorithms, VGGNet and AlexNet. With image streaming, images are transferred to the cloud for GPU computing. In addition, the Cartographer SLAM algorithms is used for the indoor simultaneous localization and mapping. The experimental results show that the accuracy of proposed face recognition system under the conditions of four different illumination is 88%, which proves the feasibility of the method. Through the cloud GPU, the local computation and processing time can be reduced. The established mobile robot system can perform the indoor navigating and simultaneous localization and mapping.