This study investigates the capability and sensitivity of a variable-grid global atmospheric model (called the Model for Prediction Across Scales-Atmosphere; MPAS-A, hereafter MPAS) in simulating the characteristics of tropical cyclones (TCs) over the South-West Indian Ocean, using two historically significant TC events (i.e., TCs Idai and Kenneth) as case studies. In the study, we first applied MPAS to simulate the TCs at a uniform resolution of 60 km over the whole globe and examined the model's capability to simulate various characteristics of the TCs (e.g., track, propagation speed, landfall time and location, storm intensity, wind-pressure relationship, and rapid intensification). Then, we investigated the sensitivity of the simulated TCs to local enhancements of the model's horizontal resolution (i.e., 15 km, 10 km, 3 km) over the South-West Indian Ocean. The sensitivity of the simulated TCs to initial condition data and to the model's physics parameterization suites (mesoscale convective suite and convection-permitting suite) was also investigated. The results show that MPAS gives realistic simulations of the TCs, except that it produces the tracks and landfalls of the TCs south of the observations and underestimates the intensities of the events. With the mesoscale reference suite, the local increase in model resolution enhances the quality of the simulated TCs for both case studies. With the convection-permitting suite, the local increase in model resolution also improves the quality of the simulated TC Idai but deteriorates that of TC Kenneth, because the scale-dependent convection scheme used in the convection-permitting suite is too slow in transporting heat and moisture up to the upper troposphere and is unable to replicate the rapid intensification of TC Kenneth. The results of the study have application in the improvement and implementation of MPAS for TC early warning systems over the South-West Indian Ocean.