This work presents a computational simulation of a single Taylor bubble rising in a vertical column of stagnant liquid. The computational simulation was based on the Navier-Stokes equations for isothermal, incompressible, and laminar flow, solved by using the open source software OpenFOAM. The two fluids were assumed immiscible. The governing equations were discretized by the volume-of-fluid (VOF) method and solved using the Gauss iteration method. Parametric mesh was used in order to improve the modeling of curvilinear geometry. Numerical solutions were obtained for the rise velocities and shapes of the bubbles which are in excellent agreement with experimental data and correlations from literature.