The PHI2 method is commonly used to perform the time-varying structural reliability analysis, and the calculation of outcrossing rate is the key to the method, to achieve sufficient accuracy it is often necessary to calculate the outcrossing rate at a large number of moments. However, for practical problems with complex limit state surfaces, the calculation of the outcrossing rate at each moment can be very time-consuming. To further improve the efficiency of PHI2 method, three strategies are proposed to be introduced in this paper to improve the efficiency of calculating outcrossing rate. First, the strategy without Cholesky decomposition is used to reduce the number of random variables, while the corresponding calculation of correlation coefficients is given. Then, the improved first order reliability method based on adaptive Kriging model (AK-FORM) is introduced to efficiently calculate the reliability index at each moment. Finally, the two dimensional integral is converted into one dimensional integral by using the dimension reduction method. The above three improvement strategies are combined with the PHI2 method, which forms an efficient time-varying reliability analysis method based on the AK-FORM method and the dimension reduction method, i.e., the K-PHI2 method. Meanwhile, only the strategy without Cholesky decomposition is combined with the PHI2 method to form the PHI2- method. The calculation results of numerical and engineering examples show that the PHI2- and K-PHI2 methods proposed in this paper have the same high accuracy as the PHI2 method, and both are better than the PHI2+ method (an improved method based on PHI2) in terms of accuracy; compared with the PHI2 and PHI2+ methods, the PHI2- method has a little improvement in efficiency, while the K-PHI2 method further greatly improves the efficiency of time-varying reliability analysis on this basis.