Abstract: The aim of this article is to generalize the best approximation problem to the case of quotient generalized 2-normed spaces. At first, a quotient 2-norm is introduced and with an example we show that the quotient 2-norm is a generalized 2-norm that it is not a 2-norm. Afterward some theorems of approximation in quotient spaces are extended to this newly introduced quotient generalized 2-normed space in order to assess their validity. 2000 Mathematics Subject Classification. Primary 46A12.