We present in this paper a computer simulation study of the phase behavior of the Gay-Berne liquid crystal model. The effect of the anisotropic attractive interactions on stabilizing orientationally ordered phases is analyzed by varying the anisotropy parameter kappa’ at fixed values of the molecular elongation parameter kappa. Molecular dynamics simulations have been performed at constant density and temperature along several isotherms and approximate transition densities are reported. It is found that, for a given value of the molecular elongation kappa=3, smectic order is favored at lower densities as kappa’ increases. When kappa’ is lowered, the smectic phase is preempted by the nematic phase. As a result, the nematic phase becomes increasingly stable at lower temperatures as kappa’ is decreased. Additionally, we have studied the liquid-vapor coexistence region for different values of kappa’ by using Gibbs ensemble and Gibbs-Duhem Monte Carlo techniques. We have found evidence of a vapor-isotropic-nematic triple point for kappa’=1 and kappa’=1.25. For temperatures below this triple point, we have observed nematic-vapor coexistence as is found for many liquid crystals in experiments.