Time-variant reliability problems are frequently encountered in engineering due to factors like material degradation or random loading modeled as stochastic processes. The PHI2 method, which employs the First Order Reliability Method (FORM), is commonly used to solve such problems. However, it requires repeated searches for Most Probable Points (MPPs), making it computationally expensive. To improve efficiency with little sacrifice of accuracy, this study proposes a First Order Time-variant Reliability Expansion (FOTRE) method, which requires only a single accurate search for the so-called “worst MPP” over the whole lifespan, thereby alleviating significantly the computational burden. It is inspired by the observation that the outcrossing rate tends to be small values at the time points with relatively large reliability indexes, thus having a negligible impact on the subsequent structural failure probability over the entire lifespan. The FOTRE method offers the adaptive accuracy of the outcrossing rate and eliminates the need for repeated MPP searches, resulting in a more efficient framework for calculating the probability of structural failure over the entire lifespan. The effectiveness and accuracy of the FOTRE method are demonstrated through numerical examples.