In this study, considering the modified preformation probability Pc to be log(10)P(c)=(A(c)-1)/3log(10)P(alpha)+c ', where P alpha and c ' are the alpha-particle preformation probability and an adjustable parameter proposed by Wang et al. [Chin. Phys. C 45, 044111 (2021)], respectively, we extend a new simple model put forward by Bayrak [J. Phys. G 47, 025102 (2020)] to systematically study the cluster radioactivity half-lives of 28 trans-lead nuclei ranging from( 222)Fr to Cm-242, which is based on the Wentzel-Kramers-Brillouin approximation and Bohr-Sommerfeld quantization condition. For com...