A new simulation method called the configurational-bias-vaporization method (CBV) is proposed which is designed for studying phase equilibria for lattice-polymer systems. A single simulation cell is used in this method where all polymers are introduced in the bottom portion of the cell upon initiation. Vaporization is then carried out by randomly eliminating a chain followed by generating a new chain through the configurational-bias method. Compositions of coexisting phases are then determined directly. The phase-equilibrium coexistence curves for polymer systems with chain lengths up to 200 have been obtained. Part of the results are compared with those from the test particle method and those reported by Madden et al. Corresponding predictions by the Flory-Huggins theory and the Freed theory have also been tested. The comparison shows that the Freed theory gives satisfactory critical temperatures while the Flory-Huggins theory shows a large discrepancy as expected. However, both theories give poor critical compositions.