In high-pressure vapor-liquid equilibrium calculations using an equation of state, two types of convergence problems may be encountered as the critical region is approached. One is the trivial solution in which compositions and densities for equilibrium phases become identical and the other is the divergence problem. In the present study, an efficient algorithm was proposed to remove these difficulties in the extended regions by introducing auxiliary loops for composition and pressure (or temperature) iterations. The algorithm was found to extend the region of convergence to near critical points efficiently without using the information on adjacent equilibrium points. (c) 2005 Elsevier B.V. All rights reserved.