There is a growing need for elderly care. One of the most important factors affecting the welfare of elderly is physical training. We aim to develop a fitness coach robot which can help elderly people in their daily physical activities. The overall scenario includes two different parts. First, a human supervisor will perform fitness motions and the robot will learn them by analyzing the behavior of the demonstrator. In the second part, the robot will demonstrate the learned gestures to elderly person and give feedbacks on the correctness of gesture which is performed by the elderly to achieve the desired performance. A humanoid robot, Nao which is produced by Aldebaran Company, will be used for this study and a 3D depth sensor, Microsoft Kinect sensor, will be utilized to analyze human gestures. The main focus of our project is the development of a successful social interaction between human and robot. The robot will perform learned physical gesture and provide feedback for the person who tries to perform the gesture. The system will analyse the gesture of the elderly. Then, the robot generates corrective verbal feedback in a socially appropriate and understandable way. The elderly corrects his gesture according to the feedback.