The instability of metal interface is an important problem in the process of implosion physical compression, which is significantly different from the traditional fluid interface instability. Due to the limitation of related theory and experimental diagnosis technology, this problem is studied still insufficiently. In order to understand in depth the perturbation growth behavior of metal interface instability, the technique for high explosive driven Rayleigh-Taylor instability experiment on the oxygen-free high conductivity (OFHC) copper is developed. The perturbation growth on OFHC copper interface with varying initial perturbation amplitude at a specific time is recorded by radiography. According to the data processing on the X-ray images, the perturbation growth behaviors of the interface at different times are obtained. The experimental results show that the larger the initial perturbation amplitude, the faster the perturbation grows, but the perturbation wavelength of the interface remains almost unchanged at the explosive loading. The perturbation on the front interface will have an effect on the back free interface, and cause some corresponding disturbance to occur on the surface, namely, on the back free interface, the position corresponding to the perturbation trough of the front interface first moves and gradually evolves into a spike, while the position corresponding to perturbation crest evolves into a bubble. The strain rate of instability perturbation growth reaches ～10⁵/s, and the perturbation amplitude of the interface increases to about 700% of the initial value at 5.26 μs. The corresponding numerical simulation results show that the normal SCG model underestimates the strength of copper and cannot well describe the stabilizing effect of material strength at this high strain rate, thereby leading to the fact that the simulation results are higher than the experimental results.