Mental addictions must be overcome as they are, mentally.
It's a matter of inner strength. The addiction has formed because you have conditioned your mind to feel particularly attracted to a certain thing. To break the addiction, you must break the mental conditioning.
How was your mind conditioned in the first place? Repetition. How do you break the conditioning? Repetition.
I'm not quite sure what you're addiction is, but the secret to breaking it is to simply repeatedly not do it. Every time you want it, don't have it. It'll be difficult at first, but eventually it'll be very easy to push the idea aside.
I quit both soda and burger joints this way.
Just realize that you can do it. It is not a matter of can or cannot... it is a matter of do or do not. Quitting is not beyond you.