Complex engineering systems such as aircraft are usually affected by uncertain factors, such as material performance degradation and time-varying loads during operation. When solving complex time-variant reliability analysis (TRA) problems, the developed methods usually cost a lot. In order to improve the efficiency of solving complex TRA problems, based on the approximating most-probable-points trajectory (AMPPT) method, the efficient approximating the most-probable-point trajectory (EAMPPT) method for TRA is proposed. According to the characteristics that the reliability of weakest part of the system determines the reliability of the system, EAMPPT takes full account of prediction values and their errors in the process of approximating the most-probable-point trajectory. A mathematical example demonstrates the effectiveness of the adaptive sampling method. EAMPPT is applied to solve TRA problems involving hydrokinetic turbine blades and the wing of the reusable aerospace during reenter. The results show that the calculation accuracy of the proposed EAMPPT and time-discretization based TRA (TDTRA) method is similar, but the number of performance function evaluations of EAMPPT is less than 3% of TDTRA.