Gibbs ensemble simulations are reported for Lennard-Jones particles with embedded quadrupoles of strength Q*=Q/(epsilon sigma(5))(1/2)=2.0 where epsilon and sigma are the Lennard-Jones parameters. Calculations revealing the effect of the dispersive forces on the liquid-vapor coexistence were carried out by scaling the attractive r(-6) term in the Lennard-Jones pair potential by a factor lambda ranging from 0 to 1. Liquid-vapor coexistence is observed for all values of lambda including lambda = 0 for Q* = 2.0, unlike the corresponding dipolar fluid studied by van Leeuwen and Smit et al. [Phys. Rev. Lett. 71, 3991 (1993)] which showed no phase transition below lambda = 0.35 when the reduced dipole moment mu* = 2.0. The simulation data are analyzed to estimate the critical properties of the quadrupolar fluid and their dependence on the strength lambda of the dispersive force. The critical temperature and pressure show a clear quadratic dependence on lambda, while the density is less confidently identified as being linear in lambda. The compressibility is roughly linear in lambda.