In this paper, a new active learning function for system reliability analysis called expected system improvement (ESI) is proposed to predict how updates on component reliability affect system reliability. To measure a change in system reliability, current and updated system reliabilities are estimated when the sign of the updated performance function is positive or negative at an added sample point. The new system active learning function is derived in cases of series, parallel and combined systems, respectively. With the proposed learning function, system reliability analysis iteratively updates a Kriging model by adding the optimal sample point to the design of experiment (DOE) of the critical performance function. An extraction strategy that selects points crucial to both component and system reliabilities is also proposed. Three numerical examples and two real engineering examples were investigated to demonstrate the efficiency and accuracy of the proposed system learning function. The validation results show that the proposed method outperforms existing methods in terms of the number of function evaluations (NFE) and computational time.