We present a systematic attempt to fit the Viking lander surface pressure cycle using a Mars General Circulation Model, MarsWRF. Following the earlier study by Wood and Paige (1992) using a one‐dimensional model, high‐precision fitting was achieved by tuning five time‐independent parameters: the albedo and emissivity of the seasonal caps of the two hemispheres and the total CO2 inventory in the atmosphere frost system. We used a linear iterative method to derive the best fit parameters: albedo of the northern cap = 0.795, emissivity of the northern cap = 0.485, albedo of the southern cap = 0.461, emissivity of the southern cap = 0.785, and total CO2 mass = 2.83 × 1016 kg. If these parameters are used in MarsWRF, the smoothed surface pressure residual at the VL1 site is always smaller than several Pascal through a year. As in other similar studies, the best fit parameters do not match well with the current estimation of the seasonal cap radiative properties, suggesting that important physics contributing to the energy balance not explicitly included in MarsWRF have been effectively aliased into the derived parameters. One such effect is likely the variation of thermal conductivity with depth in the regolith due to the presence of water ice. Including such a parameterization in the fitting process improves the reasonableness of the best fit cap properties, mostly improving the emissivities. The conductivities required in the north to provide the best fit are higher than those required in the south. A completely physically reasonable set of fit parameters could still not be attained. Like all prior published GCM simulations, none of the cases considered are capable of predicting a residual southern CO2 cap.