A new scheme for Monte Carlo simulation, Bin-CMC, that was introduced recently by Fan et al. (C. Fan, D.D. Do, D. Nicholson, J. Phys. Chem. B, 115 (2011) 10509-10517), is applied to study: (1) vapour-liquid equilibria and (2) vapour-solid equilibria. Using bins in the simulation, we are able to sample space very efficiently, with larger displacements of particles in regions where densities are low and smaller displacements in regions where densities are very high. Furthermore, by exchanging particles between bins within the simulation box, we can take full advantage of the creation/destruction feature of a grand canonical simulation (built within a canonical ensemble) which enables the system to achieve equilibrium more rapidly. To illustrate the application of the new technique, we simulate the phase equilibria of argon, nitrogen, and carbon dioxide to obtain thermodynamic properties of the fluid phases including: saturation densities of the gas and condensed phases, the saturation vapour or sublimation pressure, the enthalpy of vapourization or sublimation, and the surface tension at the interface. The new scheme is superior to the Gibbs ensemble Monte Carlo (GEMC) method because the latter suffers from the extremely low probability of exchanging particles when one box is very dense, which makes it unsuitable for the study of vapour-solid equilibria and of vapour-liquid equilibria at low temperatures.