A thermal-hydraulic code, named CUPID, has been developed for the analysis of transient two-phase flows in nuclear reactor components. A two-fluid three-field model was used for steam-water two-phase flows. To obtain numerical solutions, the finite volume method was applied over unstructured cell-centered meshes. In steam-water two-phase flows, a phase change, i.e., evaporation or condensation, results in a great change in the flow field because of substantial density difference between liquid and vapor phases. Thus, two-phase flows are very sensitive to the local pressure distribution that determines the phase change. This in turn puts emphasis on the accurate evaluation of local pressure gradient. This paper presents a new reconstruction method to evaluate the pressure gradient at cell centers on unstructured meshes. The results of the new scheme for a simple test function, a gravity-driven cavity, and a wall boiling two-phase flow are compared with those of the previous schemes in the CUPID code.