The effect of equilibrium vapor-phase pressure onto freezing of a simple fluid in a nanopore is examined. We employ a molecular dynamics (MD) technique in a unit cell with imaginary gas phase, which has the benefit of easy determination of equilibrium vapor pressure. The method is shown to give consistent results with those by the grand canonical Monte Carlo (GCMC) method, and to have better feature of smaller degree of hysteresis between freezing and melting. The MD simulations showed liquid-solid phase transitions, at a constant temperature, with the variation in the equilibrium vapor-phase pressure below the saturated one. Thus-determined solid-liquid coexistence lines exhibited significant dependence of the freezing point against small changes in the bulk-phase vapor pressure, which implies the importance of tensile effect on freezing in nanopores. The capillary effect on the shift in freezing point was successfully described by a simple model based on continuum and isotropic assumption, even in a pore as small as 2 nm in width.