Absolutely. I've met many people who are fluent in English using various methods. Tutors, living abroad, and watching TV shows over and over show the best results. However, all of those people had one thing in common: dedication.
If you spend one session per week with a Skype tutor, and do nothing between those sessions, you will probably never become fluent. It takes a lot of work, but I personally think a tutor is the best method if you can't live abroad. Watching TV shows is fantastic, but it is the most labor-intensive of the three methods. I don't have the patience to watch a TV show over and over again. :(