Kinetic Monte Carlo (kMC) simulations were carried out to describe the vapour-liquid equilibria of argon at various temperatures. This paper aims to demonstrate the potential of the kMC technique in the analysis of equilibrium systems and its advantages over the traditional Monte Carlo method, which is based on the Metropolis algorithm. The key feature of the kMC is the absence of discarded trial moves of molecules, which ensures larger number of configurations that are collected for time averaging. Consequently, the kMC technique results in significantly fewer errors for the same number of Monte Carlo steps, especially when the fluid is rarefied. An additional advantage of the kMC is that the relative displacement probability of molecules is significantly larger in rarefied regions, which results in a more efficient sampling. This provides a more reliable determination of the vapour phase pressure and density in case of non-uniform density distributions, such as the vapour-liquid interface or a fluid adsorbed on an open surface. We performed kMC simulations in a canonical ensemble, with a liquid slab in the middle of the simulation box to model two vapour-liquid interfaces. A number of thermodynamic properties such as the pressure, density, heat of evaporation and the surface tension were reliably determined as time averages.