© 2019 by Begell House, Inc. www.begellhouse.com The authors have developed a numerical simulation code for gas-liquid two-phase flows with a high-precision volume-of-fluid-type interface-tracking method on unstructured meshes. In this paper, we propose an improved pressure calculation method in the vicinity of a gas-liquid interface based on the balanced-force algorithm, which was originally developed on structured meshes. To achieve accurate calculations for interfacial dynamics, we introduce the concept of external force potentials to take into account the physically appropriate mechanical balance between the pressure and the external forces, i.e., the surface tension and the gravitational force, at the gas-liquid interfaces. The validity of the improved pressure calculation method is checked by simulating a spherical bubble in stationary liquid and a rising bubble in liquid. As a result, the improved pressure calculation method succeeds in highly suppressing unphysical behavior, i.e., the spurious velocity, compared to the conventional simulation method. Therefore, the improved pressure calculation method on unstructured meshes is considered to work well in numerical simulations of gas-liquid two-phase flows.