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The traditional constant‐stress accelerated life test may encounter the problem of no or a few failures at the low stress level, if the test is stopped after a fixed period. Insufficient failures usually make it difficult to estimate reliability characteristics and to discover design deficiencies of the product. To mitigate the problem, the adaptive plan is designed based on Bayesian methods in this study. Under the constraints of test facilities, test units, time, and cost, the adaptive plan is optimized according to the criterion of minimizing the preposterior variance of the logarithm of a quantile of the lifetime distribution at the use condition. Large‐sample approximation is applied to reduce the computational burden. Genetic algorithm is adopted to determine the optimal design of the adaptive plan. Finally, a numerical example is given to demonstrate the advantages of the proposed adaptive plan.