This study systematically investigates the statistics of the centreline small-scale turbulence of a circular jet issuing from a smooth contraction nozzle. Detailed velocity measurements were performed for the exit Reynolds number of Re=20100, where Re≡Ujd /ν with Uj being the exit mean velocity, d the nozzle diameter and ν the kinematic viscosity. After effectively filtering out high frequency noises, statistical properties of the small-scale turbulence were obtained appropriately; those properties include turbulence energy dissipation rate, Kolmogorov length scale, Taylor scale, turbulence Reynolds number, skewness and flatness of the velocity derivative. It is observed that these properties satisfy their self-preserving relations in the far field. It is also revealed that the small-scale turbulence reaches the self-preserving state earlier than does the large-scale motion. Besides, the smallest-scale turbulence depends least on the initial and boundary conditions and therefore behaves most universally across different flows.