Mixtures of molecular fluids are encountered often in chemical industry, and the vapor-liquid coexistence curves are required for efficient design of separation processes. Hence, a computational scheme employing the Wang-Landau and grand canonical transition matrix Monte Carlo molecular simulation techniques is used for the first time to compute the fluid phase diagrams of molecular mixtures. Binary mixtures of n-alkanes, viz., methane-ethane, ethane-propane, propane-n-butane systems, are studied here as examples of molecular mixtures. The total molecule number probability distribution, obtained from the GC-TMMC simulations, allows us to directly calculate coexistence properties such as pressure, density, and composition. On comparison with experimental data, reported in the literature, it was observed that the predicted VLE properties, with the exception of pressure, are in close agreement with the corresponding experimental values. The deviation of calculated pressure from experiments could be attributed to the use of the TraPPE-UA force field where such behavior has already been reported for pure component systems. The above methodology has been coupled to the Binder cumulant intersection technique to derive the critical properties of the mixture when one of the components is supercritical. The critical properties obtained from our simulations are a good match to those obtained from experiments. Thus, our work shows that the transition matrix methods are able to predict properties in the critical region with remarkable accuracy where other traditionally employed simulation methodologies are not very successful.