High-temperature steam electrolysis (HTSE) is a promising method for highly efficient large-scale hydrogen production. The HTSE process not only reduces the amount of thermodynamic electrical energy requirement but also decreases the polarization losses, which improves the overall efficiency of hydrogen production. In this paper, a two-dimensional simulation method of the efficiency of the HTSE system integrated with high-temperature gas-cooled nuclear reactor (HTGR), which changes two parameters simultaneously in a reasonable range while keeping one parameter constant, was presented. Compared with one-dimensional analysis method, the effects of electrical efficiency (eta(el)), electrolysis efficiency (eta(es),), and thermal efficiency (eta(th)) on overall efficiency (eta(overall)) were investigated more objectively and accurately. Moreover, the critical concepts of eta(es) and eta(th) were put forward originally, which were very important to determine the optimum electrolysis voltages and operation temperatures in the actual HTSE processes. The calculated critical value of eta(es) was Delta G(T)/Delta H(T) and the actual eta(es) should be higher than the theoretically calculated one in order to maintain the high hydrogen production efficiency of HTSE system. Also, it was very interesting to find that the critical eta(th) was the theoretical maximum efficiency in SOFC mode. Furthermore, the critical value of eta(th) was equal to the value of eta(el), which means the overall efficiency decreases with the eta(es) increasing if the eta(th) in the actual HTSE process is less than the critical value of eta(th). Therefore, it is very important to control the eta(th) higher than the critical value in the actual HTSE process to get high overall system efficiency. (C) 2008 Elsevier B.V. All rights reserved.