Gröbner-Shirshov bases and reduced form of the elements were already found the Coxeter groups of type $A_n, B_n$ and $D_n$ in [1]. They also proposed a conjecture for the general form of Gröbner-Shirshov bases for all Coxeter groups. In [2] , an example was given an to show that the conjecture is not true in general. The Gröbner-Shirshov bases of the other finite Coxeter groups are given in [3] and [4]. This paper is another example of finding Gröbner-Shirshov bases for groups, defined by generators and defining relations.In [5], we calculated Gröbner-Shirshov Basis and reduceds words for $\tilde{A}_n$. In this talk, we deal with the affine Weyl group $\tilde{C}_n$ which is an infinite Coxeter group. Using defining relations, we able to find the reduced Gröbner-Shirshov bases of $\tilde{C}_n$ and classify all reduced words of the affine Weyl group $\tilde{C}_n$