The First Order Reliability Method (FORM) of structural reliability analysis involves the calculation of the function value and gradient value of the iteration point in each iteration, but the subsequent iteration process cannot make full use of the calculation results of the iteration point in the previous iteration process, the calculation efficiency thusly needs to be further improved. Considering that the iteration points fluctuate in the local area in the later iteration, if the surrogate model is established upon the existing iteration results to calculate the function value and gradient value of the iteration point in the later iteration, it will help to improve the calculation efficiency of the FORM. To this end, the iterative process of FORM is divided into a global search stage and a local search stage, and they are applied in different calculation strategies. In the local search stage, a Kriging model is established upon the iteration results in the global search stage, and a learning function that can evaluate the accuracy of the Kriging model at the iterative points is introduced to realize the efficient calculation of the iterative points in the local search stage, and an improved FORM with high computational efficiency is proposed. The calculation results of numerical examples and engineering examples show that the method proposed can significantly improve the computational efficiency of the FORM just of keeping the accuracy unchanged.