High-order harmonic generation from a solid surface affected by the contrast of a laser pulse was studied using an oscillating mirror model. High-order harmonics generated from solid surfaces have unusual properties such as spectral redshift, and an intensity difference between even- and odd-order harmonics which is not reported for high-order harmonics generated by a gas medium. We confirmed that high-order harmonics from solid surfaces have selectivity of polarization as well as cut-off extension and the enhancement of conversion efficiency proportional to laser intensity. And the principle of operation and the characteristics of a plasma mirror system developed for achieving high contrast laser pulses to pursue the experimental realization of high-harmonic generation from solid surfaces are reported. Energy fluence on the plasma mirrors is tunable between $10;J/cm^2$ and $1000;J/cm^2$ and around 1000 shots are available before the plasma mirrors require replacement.