Planar shock compression experiments are performed on a Zr-based bulk metallic glass (BMG), Zr51Ti5Ni10Cu25Al9 at peak shock stresses from 10 GPa to 27 GPa to investigate its plastic behavior under high pressure and high strain-rate. The particle velocity profiles measured at the free surface of the samples are analyzed to estimate longitudinal stresses of the Zr-based BMG in the shock loading process,and then shear stresses are obtained by comparing longitudinal stresses with a hydrostat. Though there is an obvious relaxation effect after elastic front, the Hugoniot elastic limit of the Zr-based BMG is found to increase with shock stress increasing. However, the shear stresses across the plastic shock front display stress hardening above the Hugoniot elastic limit followed by a stress relaxation (softening) to Hugoniot state, and the relaxation level also increases with shock stress increasing. The changes of shear stresses under planar shock compression are consistent with the results from molecular dynamic simulations, but obviously different from the pressure-shear impact experimental results or uniaxial stress impact experimental results.