The 21st century is the world of technology where most people do not even imagine their life without technology. Social networking sites refer to various applications, websites or new online media that allows large numbers of individuals to share their information and develop a proper social and specialized contact. These sites emphasize the creation of a connection between people to enable them to share their interests. However, sharing of information and creating connections with unknown persons has sometimes a key concern of security which get arised with our action on Social Media. The paper analyses the growing security concerns in Social Media and lay down some measures which will help users to enjoy and ensure smooth and safe social networking.