The spectral characteristics of high-order harmonics generated by the interaction of a linearly polarized relativistic laser pulse with a plasma grating target are investigated. Through particle-in-cell simulations and an analytical model, it is shown that a plasma grating target with periodic structure can select special harmonics with integer multiples of the grating frequency, and that low-order harmonics with frequencies being integer times of the laser frequency are generated nearly parallel to the target surface from a Fresnel zone plate target with an aperiodic structure. Spectral control of the harmonics can be achieved by introducing a correction factor β to the radius formula of the Fresnel zone plate, which can create a slightly detuned plasma grating, and then only the narrow-band harmonics can be selected nearly parallel to the target surface. The center order of the narrow-band harmonics can be tuned by adjusting the correction factor β, while the bandwidth of the harmonics can be selected by adjusting the other parameter λ_{f} of the detuned plasma grating.