The interfacial RT instability experiments on imploding jelly liners in cylindrically convergent geometry have been performed. The liner's instability growth was observed clearly with a high-speed framing camera. Jelly liners have different initial perturbation forms on their inner and outer interfaces, being either smooth or sinusoidal. The initial perturbations also have different magnitudes and spatial frequencies (for example, mode n=5, 10, 20). The experimental results show that the growth and coupling of perturbations on inner and outer surfaces are remarkably different.Meanwhile, the relevant 2-D numerical simulation of hydrodynamics combined with Level Set method has been performed. Using the numerical code, we can design the parameters of imploding jelly liner, and predict the experimental results. The results of simulation are demonstrated to be in good agreement with the measured data in a series of experiments.