REX-10 is a fully-passive small modular reactor in which the coolant flow is driven by natural circulation, the RCS is pressurized by a steam-gas pressurizer, and the decay heat is removed by the PRHRS. To confirm design decisions and analyze the transient responses of an integral PWR such as REX-10, a thermal-hydraulic system code named TAPINS (Thermal-hydraulic Analysis Program for INtegral reactor System) is developed in this study. Based on a one-dimensional four-equation drift-flux model, TAPINS incorporates mathematical models for the core, the helical-coil steam generator, and the steam-gas pressurizer. The system of difference equations derived from the semi-implicit finite-difference scheme is numerically solved by the Newton Block Gauss Seidel (NBGS) method. TAPINS is characterized by applicability to transients with non-equilibrium effects, better prediction of the transient behavior of a pressurizer containing non-condensable gas, and code assessment by using the experimental data from the autonomous integral effect tests in the RTF (REX-10 Test Facility). Details on the hydrodynamic models as well as a part of validation results that reveal the features of TAPINS are presented in this paper.