The aim of this paper is to investigate the symmetry problem of a class of fractional Schrödinger equations in bounded annular domains. The fractional Schrödinger equations will be transformed into a system of integral equations involving Bessel potentials and Riesz potentials. Then via the methods of moving planes and Hardy-Littlewood-Sobolev inequality, this paper proves that the annular domains must be balls with the same center, and provided that the boundary values of these equations are constants, positive solutions of this system must be radially symmetric and decreasing with the distance from the center.