Numerical investigation of two-phase loop thermosyphon (2PLT) in steady and transient states is addressed. A one-dimensional two-phase flow model describing a liquid-gas mixture in both mechanical and thermal equilibrium but out of thermodynamic equilibrium is developed. The model considers subcooled liquid and over heated vapor as well as phase transition (evaporation and condensation). The flow model is solved with a specific hyperbolic solver based on Godunov method and Harten-Lax-van Leer-Contact (HLLC) Riemann solver. A parametric study on the thermal power at the evaporator is performed in steady and transient states, the aim being to determine the effects of thermal power increase at the evaporator on the loop behavior. The comparison between Goodwin and Stiffened Gas (SG) equation of state (EOS) models shows fair agreement for latent heat of vaporization, specific volume and enthalpy for both liquid and vapor phases. Simulation of four test cases, corresponding to different evaporator thermal loads, is also carried out in transient state showing that loop response is correctly reproduced by this numerical approach, novel in the context of thermosyphon loops.