A quasi-two-dimensional (2D) Stockmayer model is developed in which the center of mass of the molecule is confined on a plane while the dipole of the molecule can rotate freely in three dimensional space. This model entails essential characteristics of systems such as dipolar molecules physisorbed on a solid surface, or a Langmuir monolayer consisting of short-chain molecules with a dipolar tail. The Gibbs ensemble Monte Carlo technique is employed to determine the vapor-liquid equilibria of the model fluids. An Ewald sum for this quasi-2D model is formulated to account for the long-range dipolar interactions. Three systems with different reduced dipole moments were studied. The critical point of each system is determined by fitting the vapor-liquid coexistence data to a 2D scaling law and the rectilinear law. We find that in general the critical temperature of the system is reduced due to the confinement and is sensitive to the strength of the dipole moment, whereas the critical density is not. The effect of reducing the dispersion part of potential on the vapor-liquid equilibria is also studied We find the dispersion potential reduction leads to a lower critical temperature and a higher in-plane part of molecular dipole moment; however, because the reduced critical temperature is relatively small compared with that of a 3D system, disappearance of the critical point is not observed in the quasi-2D SM system within practical scope of the simulation.