In this paper we apply a general variable neighbourhood search (GVNS) to the cyclic bandwidth sum problem (CBSP). In CBSP the vertices of a graph must be laid out in a circle in such a way that the sum of the distances between pairs of vertices connected by an edge is minimized. GVNS uses different neighbourhood operations for its shaking phase and local search phase. Also the initial solution is improved using random variable neighbourhood search. Extensive experiments were carried out on classes of graphs with known results for which optimal values of cyclic bandwidth sum was achieved. On other classes of graphs, values less than known upper bounds were achieved.