We are concerned with the bosonic sector of an Nu = 2 supersymmetric Chern-Simons-Higgs theory in 2 + 1 dimensions. Here the gauge group is SU (N) x U (1) and has N-f flavors of fundamental matter fields. Recently, Chen, Han, Lozano, Schaposnik showed the existence of two gauge-distinct solutions carrying the same physical energy on a two dimensional flat torus. In this paper, we find a solution which has a different asymptotic behavior from Chen, Han, Lozano, Schaposnik's result.