Is there such thing as food addiction?

Yes. Eating disorders may take the form of 1) compulsive overeating, 2) bulimia with purging or 3) anorexia nervosa. All three of these disorders are forms of food addiction.
Recent research. There is no generally accepted diagnostic category of "food addiction" other than the what was previously mentioned. However, recent research is suggesting that for some people food can create the same neurochemical responses--and likely dependence--as drugs or alcohol. So as research is mounting to support this issue, medical professionals are beginning to accept and treat it as a real illness.