We investigate the eigenvalues of the semi-circulant preconditioned matrix for the finite difference scheme corresponding to the second-order elliptic operator with the variable coefficients given by $L_vu;:=-{Delta}u+a(x,;y)u_x+b(x,;y)u_y+d(x,;y)u$, where a and b are continuously differentiable functions and d is a positive bounded function. The semi-circulant preconditioning operator $L_cu$ is constructed by using the leading term of $L_vu$ plus the constant reaction term such that $L_cu;:=-{Delta}u+d_cu$. Using the field of values arguments, we show that the eigenvalues of the preconditioned matrix are clustered at some number. Some numerical evidences are also provided.