Iron under extreme compression widely exists in celestial bodies such as the Earth, super-Earths and stars. The analysis of the composition and evolution of celestial bodies depends on the accurate cognition of material characteristic parameters. However, under the concerned TPa pressure, the equation of state(EOS) of iron equation of state given by different theoretical models are obviously different, so high-precision equation of state experiments are needed to verify the theoretical models. The research team of material compression characteristics of Laser Fusion Research Center carried out the shock Hugoniot experiment on a 100kJ-level laser facility, and obtained high-quality Hugoniot data of iron by loading a 100-micron thick target sample with long pulse radiation shock with the impedance matching method. The pressure range of experimental data is 3.5 ~ 8TPa, and the uncertainty of shock wave velocity measurement is 0.5 ~ 0.8%. Comparing the experimental data with the theoretical data, our high-precision experimental data can effectively identify the theoretical models. Our high-precision experimental results establish an important benchmark equation of state of iron, which plays an important role in promoting the inspection and development of theoretical models.