When high-speed vehicles enter into the atmosphere, plasma sheath may be excited around due to aerodynamic heating, resulting in difficulties in communicating and changes of electromagnetic scattering properties. Those facts have received lots of attention due to their influences on the aerospace communication and radio telemetry applications. While analytic and numerical studies have been carried out by many native institutions on the electromagnetic radiation/scattering problems in the presence of plasma sheath, there remains the lack of measurement data to support and verify those researches. This work reports the backscattering measurements for the target surrounded by plasma sheath in the ground high-enthalpy shock tunnel facility. Using the step frequency sweeping mode of a commercial instrument, i.e., vector network analyzer, we conduct the experiments in the JF-10 high-enthalpy shock tunnel. The dynamic electromagnetic scattering measurement must be completed on a time scale of ms while the shock tunnel is running. The implementation details are demonstrated in this work, including the experimental configurations, data processing procedures, timing synchronization, and discussion on the relationships between the air flow status and measured target scattering signals. The influences of the plasma sheath on the target RCS (radar cross section) in the C band are successfully and clearly observed. The influence of the air flow status on the measured data can be concluded as follows: the front section of high-speed air flow lasting about 0.5-1 ms will change the measured signal dramatically, which should be avoided in observation due to its instability; the effective plasma sheath lasts only about 2 ms, resulting in an overall reduction on the target RCS by about 2 dB in the measurements. Afterwards, the effects by the plasma sheath on the target scattering vanish quickly.