The problem is big: 7,250,000,000 Pounds – that is the estimated amount of plastic in our oceans. Boyan Slat is a student of the university in Delft (NL) and he came up with a solution for this problem.
So far there is only a concept and a theory how to clean the oceans but in this TED-Talk you can see that this project is realizable:
He tells a lot of different problems like how to handle the plastic while it is moving around, what about by-catches and the emission of the cleaning vessels. The nice thing about this is, that he already has solutions for those problems. It just need some further researches and money. If you would like to know more about this. I can recommend the TED-Talk and this website: boyanslat.com