In the present article, series of experiments were conducted to study the structure characteristics of premixed flames in turbulent rich hydrogen-air mixtures within a constant-volume turbulent combustion system, 7 equivalence ratios (1.2, 1.4, 1.6, 1.8, 2.0, 2.2, and 2.5), and 5 turbulent intensity (0, 0.494, 0.742, 1.080, and 1.309m/s) were studied. With the increase of turbulent intensity, the cellularity degree was obviously enhanced for turbulence promoted the formation and the development of initial cracks by wrinkling flame-front; furthermore, the enhanced hydrodynamic instability was also one important reason. Turbulence would change the linear growth of critical radius to equivalence ratio into nonlinear, but the variation extents had limitation. The wrinkling index of flame-front would rise as flame expanded, and the wrinkling index on flames with similar size would be increased with the increase of turbulence once the turbulent intensity was sufficiently high. From the variations of the root mean square of related oscillation on flame-front, it could be found that the partial amount of oscillation induced by sole turbulence was declined as flame expanded for the breakup of large eddies.