Dynamic reliability measures reliability of an engineered system considering time-variant operation condition and component deterioration. Due to high computational costs, conducting dynamic reliability analysis at an early system design stage remains challenging. This paper presents a confidence-based meta-modeling approach, referred to as double-loop adaptive sampling (DLAS), for efficient sensitivity-free dynamic reliability analysis. The DLAS builds a Gaussian process (GP) model sequentially to approximate extreme system responses over time, so that Monte Carlo simulation (MCS) can be employed directly to estimate dynamic reliability. A generic confidence measure is developed to evaluate the accuracy of dynamic reliability estimation while using the MCS approach based on developed GP models. A double-loop adaptive sampling scheme is developed to efficiently update the GP model in a sequential manner, by considering system input variables and time concurrently in two sampling loops. The model updating process using the developed sampling scheme can be terminated once the user defined confidence target is satisfied. The developed DLAS approach eliminates computationally expensive sensitivity analysis process, thus substantially improves the efficiency of dynamic reliability analysis. Three case studies are used to demonstrate the efficacy of DLAS for dynamic reliability analysis.