This paper examines the feasibility of using periodically varying dielectric layers with dielectric constant ${epsilon}_1$ and ${epsilon}_2$ at millimeter wave frequency for implementing the frequency-selective reflectors that permit feed separation in large aperture reflecting antenna systems. For oblique incidence, it is found that the total reflection can be obtained at different frequencies for proper choices of ${epsilon}_1$, ${epsilon}_2$ and the geometric parameters. In the frequency-selective reflector designed, the bandwidth for 90% reflection is always found to be much narrower than that for 90% transmission.