Let R; S; T be subsets of a group G such that = , and e . Define the undirected graph SC(G;R; S; T) to have vertex set G×{0; 1}, and with vertices (h; i), (g; j) adjacent if and only if one of the following three possibilities occurs: (1) i = j = 0 and R; (2) i = j = 1 and S; (3) i = 0; j = 1 and T. The graph SC(G;R; S; T) is called a semi-Cayley graph. Equivalently, a semi-Cayley graph may be defined as a graph = (V;E) which admits an automorphism group acting semiregular on the vertex set V with two orbits (of equal size). Let be a graph with vertices labeled as . The adjacency matrix A( ) of is an n × n matrix with (i; j)-entry equals to 1 if vertices i and j are adjacent and 0 otherwise. The spectrum of a graph is the set of numbers which are eigenvalues of A( ), together with their multiplicities. .We derive a formula of the spectrum of semi-Cayley graphs over _nite abelian groups. As an application of our main result, we give a method to construct integral graphs. In particular, we obtain an explicit expression for the spectrum of Cayley graphs over two non-abelian groups (dihedral groups and dicyclic groups). We give the spectrum of Cayley graphs over dihedral groups and dicyclic groups , respectively.