It is known that if there exists a Gröbner-Shirshov basis for a group G, then we say that one of the decision problem, namely the word problem, is solvable for G as well. Therefore, as the main target of this paper, we will present a (non-commutative) Gröbner-Shirshov basis for the braid group associated with the congruence classes of complex reflection group G 12 which will give us normal forms of the elements of G 12 and so will obtain a new algorithm to solve the word problem over it