Based on scanning-electron microscopy, the lower resolution images were collected to show macro pore properties while the high resolution images were collected to show micro pore properties, and Markov chain Monte Carlo ( MCMC ) method was used to construct the corresponding macro pore and micro pore digital rock respectively. Then superposition method was used to construct carbonate dual pore digital rock. Finally, pore structures of digital rocks were compared. The results show that MCMC method could reconstruct the 3D digital rock quickly. The carbonate dual pore digital rock construeted by superposition method has a higher percolating volume fraction, which shows that micro pore has an important influence on the total connectivity. The carbonate digital rock constructed by superposition method has a himodal pore size distribution which could describe the macro pore and micro pore characteristics simultaneously.