Mac Book Pro 15" Retina shuts down

I have a Mac Book Pro 15" with Retina display that shuts down when on battery power when remaining at 30-40% battery and when I try to start it, on the screen appears that empty battery that is telling me to plug in to power, like the battery would be fully discharged. I tried also to wait for 20-30 minutes and then try to start it, but the same battery appearing on the black screen. When I plug the Mac Book to power, it starts up, and the battery percentage is at the value that was when it shut down (30-40 %). Can someone tell me what could be the problem? Is the battery the problem? Thank you