A new sequential sampling method, named sequential exploration-exploitation with dynamic trade-off (SEEDT), is proposed for reliability analysis of complex engineered systems involving high dimensionality and a wide range of reliability levels. The proposed SEEDT method is built based on the ideas of two previously developed sequential Kriging reliability methods, namely efficient global reliability analysis (EGRA) and maximum confidence enhancement (MCE) methods. It employs Kriging-based sequential sampling to build a surrogate model (i.e., Kriging model) that approximates the performance function of an engineered system, and performs Monte Carlo simulation on the surrogate model for reliability analysis. A new acquisition function, referred to as expected utility (EU), is developed to sequentially locate a computationally efficient set of sample points for constructing the Kriging model. The SEEDT method possesses three technical contributions: (i) defining a new utility function with several desirable properties that facilitates the joint consideration of exploration and exploitation over the course of sequential sampling; (ii) introducing a new exploration-exploitation trade-off coefficient that dynamically weighs exploration and exploitation to achieve a fine balance between these two activities; and (iii) developing a new convergence criterion based on the uncertainty in the prediction of the limit-state function (LSF). The effectiveness of the proposed method in reliability analysis is evaluated with several mathematical and practical examples. Results from these examples suggest that, given a certain number of sample points, the SEEDT method is capable of achieving better accuracy in predicting the LSF than the existing sequential sampling methods.