Aiming at the spatial-temporal search problem of how to find the missing target quicklya recursive Bayesian method based search decision-making framework and an adaptive search strategy are proposed.In the decision-making frameworkthe upper limit of the searchers speedthe possibilities of false alarm detection and missed detection of the sensor are taken into considerationand the expression of the confidence function evolution under the decision framework is theoretically derivedbased on which an effective search theory is proposed.Since the impact of different strategies on decision-making can be studied and compared under this decision-making frameworkit provides an effective platform for comparison and analysis of different strategies.Finallythe effectiveness and practicability of the decision framework and proposed strategy are verified by a large number of numerical simulations.