The Johnson–Cook (JC) flow stress model can simply express the strain-rate and temperature dependencies of the flow stress. We previously proposed a concept of a simple identification method for material constants in the JC model associated with the strain-rate and temperature sensitivities (JC parameters C and m) at high-strain rates. However, several issues still exist in our method for practical use. In this study, we modified our method to identify both the JC parameters C and m. The fundamental concept was formulated based on the requirement that the normalized indentation depths obtained from the ball impact and instrumented ball indentation tests are equal to each other. In addition, the conversion factor was derived to transfer from the impact velocity to the strain rate. The ball indentation and impact analyses based on a finite element method were conducted to verify the established method. The analysis results obtained under idealized conditions demonstrated that C and m can be accurately identified using the established method, even at exceeding 104 s−1. Changes in the radius of the impactor are more effective in obtaining different strain rates than changes in the impact velocity because the identification accuracy can be ensured at lower than 200 m/s.