We have studied the influence of the distribution of bimodal bonds on the phase transition in two-dimensional 8-state Potts model by the recently proposed Wang-Landau (WL) and the Swendsen-Wang (SW) algorithm. All simulations and measurements are done for r = 0.5 Physical quantities such as energy density and specific heat are evaluated at all temperatures. We have also obtained the probability distributions of the energy in order to monitor the transitions. We have observed that some cases of the periodically arranged bond distributions show a single peak, and some cases show double or triple peaks in the specific heat. Besides, it seems that the appearing of these peaks in the specific heat relates to blocking procedure for periodicity. When the number of interaction pairs between the bimodal bonds is increased on the lattice with the blocking procedure, one can observe a single peak, otherwise, on can observe a double or triple peaks in the specific heat. From the point of view of simulation methods, the WL algorithm also works efficiently in the simulation of the system for a periodically arranged bond distribution as well as the SW algorithm.