When adaptively selecting training point in Kriging model based time-dependent reliability analysis, existing methods may lose efficiency due to less considering the Kriging prediction correlation at different time instant as well as the interaction of random input and time variable. Thus, a novel training point selection strategy is proposed by maximizing structural state misclassification probability (SSMP) reduction. Firstly, by taking the Kriging prediction correlation at different time instant into account, the SSMP is derived for random input candidate sample. Secondly, since it is inefficient to actually evaluate SSMP, the expected SSMP is approximately derived with the current Kriging model information by virtually adding the random input and time candidate sample pair into training set. Then, the SSMP reduction, i.e., the difference between the SSMP derived in first step and the expected SSMP in the second one, can be evaluated. By actually adding the random input and time candidate sample pair with the maximum SSMP reduction into training set, the novel training point selection strategy is proposed to update the Kriging model for minimizing SSMP expectedly. Due to considering the Kriging prediction correlation in deriving SSMP, as well as the interaction of random input and time in evaluation the SSMP reduction, the maximum SSMP reduction guided training point selection strategy is superior to the up-to-date methods. The presented example results show that the proposed method needs a least number of evaluating performance function in four compared adaptive Kriging model based methods, and the reduction number of evaluating performance function of the proposed method with respect to the up-to-date methods is more in complex engineering examples than in the simple numerical ones.