Let F 2 m be a finite field of cardinality 2 m, R= F 2 m+ u F 2 m (u 2= 0) and s, n be positive integers such that n is odd. In this paper, we give an explicit representation for every self-dual cyclic code over the finite chain ring R of length 2 s n and provide a calculation method to obtain all distinct codes. Moreover, we obtain a clear formula to count the number of all these self-dual cyclic codes. As an application, self-dual and 2-quasi-cyclic codes over F 2 m of length 2 s+ 1 n can be obtained from self-dual cyclic code over R of length 2 s n and by a Gray map preserving orthogonality and distances from R onto F 2 m 2.