An intrinsic time-dependent one-dimensional (1D) model and a macro two-dimensional (2D) model for the anode of the direct methanol fuel cell (DMFC) are presented. The two models are based on the dual-site mechanism, which includes the coverage of intermediate species of methanol, OH, and CO (θ M , θ OH,Ru , and θ CO,Pt ) on the surface of Pt and Ru. The intrinsic 1D model focused on the analysis of the effects of operating temperature, methanol concentration, and overpotential on the transient response. The macro 2D model emphasises the dimensionless distributions of methanol concentration, overpotential and current density in the catalyst layer which were affected by physical parameters such as thickness, specific area, and operating conditions such as temperature, bulk methanol concentration, and overpotential. The models were developed and solved in the PDEs module of COMSOL Multiphysics, giving good agreement with experimental data. The dimensionless distributions of methanol concentration, overpotential, and current density and the efficiency factor were calculated quantitatively. The models can be used to give accurate simulations for the polarisations of methanol fuel cell.