The investigation of hydrodynamic instability growth in convergent geometry is crucial for optimizing the design of inertial confinement fusion capsules, which aims to mitigate the growth of hydrodynamic instability and mixing. Experiments about the hydrodynamic instability of the decelerated inner interface in radiation-driven cylindrical implosions were conducted at 100 kJ laser facility. Mode coupling of perturbations and the Bell-Plesset (BP) effect unique to convergent geometry were observed. The theoretical predictions of the growth induced by the BP effect are consistent with the experimental results. Additionally, these experiments identified a second-order mode introduced by an M2 drive asymmetry. The drive asymmetry is about 11%. To mitigate the drive asymmetry, a method of extending the length of the hohlraum was proposed. Researches of the hydrodynamic instability in cylindrical geometry contribute to a better understanding of how convergent geometry affects hydrodynamic instability growth at high energy density, thereby aiding in optimizing the design of inertial confinement fusion capsules.