FORTRAN code for the cluster Monte Carlo study of the $q$-state Potts model on $D$-dimensional hypercubic lattices. Solution method: The Swendsen and Wang’s algorithm is used to simulate equilibrium bond configurations of the q-state bond-correlated percolation model (QBCPM) corresponding to the QPM. Based on the bond-configuration, the lattice sites are classified into different clusters via the multiple labeling technique of Hoshen and Kopelman. Hu’s connection between the geometrical quantities of the QBCPM and the physical quantities of the QPM is used to calculate physical quantities of the QPM.