The cluster radioactivities of trans-lead nuclei are systematically investigated by using the effective liquid drop description with the varying mass asymmetry shape and effective inertial coefficient. An effective nuclear radius constant formula is used instead of the original empirical formula in calculation. The calculated half-lives are in good agreement with the available experimental data. The root-mean-square deviation between the calculated logarithmic half-lives and the experimental ones is only 0.895. From the plots of the calculated lgT1/2 values versus the neutron (or proton) number of daughter, the shell effect of neutron magic number N=126 (or proton magic number Z=82) can be clearly seen. The odd-even-stagger can be clearly seen in the odd clusters 25Ne, 29Mg. The calculated half-lives conform to the Geiger-Nuttall law. We obtain some important conclusions about the Geiger-Nuttall law from the calculated results.