Passive systems are widely becoming used in the nuclear industry to improve the safety level of nuclear power plants. However, the functioning parameters of the passive systems are extremely tied to uncertainty, and the reliability assessment of these systems is one of the important open issues in the passive safety system analysis area. So far, there is no common method to estimate the reliability of passive safety systems. The FORM method with the HL-RF algorithm is a popular iterative method to gain reliability index. However, when the nonlinearity of a system increases, the method may cause numerical instability. In this study, the reliability methodology for passive safety systems (RMPS) is applied to evaluate the reliability of the passive heat removal system (PHRS) of the VVER-1000 reactor. A simple and efficient reliability algorithm is proposed to overcome the numerical instabilities of the HL-RF algorithm of FORM based on the effective search direction vectors with an appropriate step size to find the design point. The accuracy of the proposed algorithm is shown through the stochastic response surface method (SRSM). Results show that the proposed algorithm is simple, reliable, fast, and can find the reliability index with high efficiency and accuracy.