Laser-driven ramp compression was used to investigate iron characteristics along the isentropic path.The iterative Lagrangian analysis method was employed to analyze the free surface velocity profiles in iron stepped target measured with two VISARs.The onset stress for the α to ε phase transformation was determined from the sudden change in the sound velocity and was found over-pressurized compared to the static and shock results.The derived stress (26 GPa) and strain rate (up to 108 S-1) are consistent with our previous experimental results.The stress-density relations were compared with those from previous ramp experiments and good agreements were found,which experimentally confirms the simulations,showing that iterative Lagrangian analysis can be applied to the ramp-compression data with weak shock.