To improve the efficiency of Kriging based structural reliability analysis, a new adaptive learning function VF is proposed after analyzing the weakness of existing learning functions. The learning function VF combines variance and joint probability density function both of which can affect the accuracy of estimated failure probability. This method can avoid wasting samples caused by sampling in the area where the value of joint probability density function is low, and increase learning efficiency. Firstly, a large number of candidate sample points are generated by Monte Carlo method, and the point that maximizes the proposed learning function value is defined as the best one. Secondly, a suitable stopping condition is proposed, which can not only ensure the accuracy of failure probability but also reduce iterations dramatically. Finally, two numerical examples are analyzed to show that the proposed method requires fewer calls to the performance function than other methods and it has high convergence speed, good accuracy and stability. And the method can be used in engineering problems with implicit and high nonlinear performance function.