Life-cycle reliability analysis can effectively estimate and present the changes in the state of safety for structures under dynamic uncertainties during their lifecycle. The first-crossing approach is an efficient way to evaluate time-variant reliability-based on the probabilistic characteristics of the first-crossing time point (FCTP). However, the FCTP model has a number of critical challenges, such as computational accuracy. This paper proposes an adaptive first-crossing approach for the time-varying reliability of structures over their whole lifecycle, which can provide a tool for cycle-life reliability analysis and design. The response surface of FCTP regarding input variables is first estimated by performing support vector regression. Furthermore, the adaptive learning algorithm for training support vector regression is developed by integrating the uniform design and the central moments of the surrogate model. Then, the convergence condition, which combines the raw moments and entropy of the first-crossing probability distribution function (PDF), is constructed to build the optimal first-crossing surrogate model. Finally, the first-crossing PDF is solved using the adaptive kernel density estimation to obtain the time-variant reliability trend during the whole lifecycle. Examples are demonstrated to specify the proposed method in applications.