For the dynamic reliability analysis of complex nonlinear bridge structures under stochastic ground motions, an efficient seismic reliability analysis method was developed based on the principle of maximum entropy. First, the relationship between the seismic reliability and extreme value distribution (EVD) of bridges was clarified. The seismic reliability of bridge structures was transformed into the corresponding EVD estimation. Then, the maximum entropy method (MEM) for estimating the EVD of nonlinear seismic responses of complex bridge structures was established. In view of the fact that the iterative solution of the existing MEM is greatly affected by the initial value and is not easy to converge, a method based on likelihood function was proposed to solve the EVD and seismic reliability of bridge structures more efficiently. Finally, a typical high-pier and long-span continuous rigid frame bridge was taken as an example. The accuracy and efficiency of the proposed method were verified via Monte Carlo simulation, and the results were compared with the results of kernel density estimation (KDE) and lognormal distribution fitting. Results show that the proposed MEM based on likelihood function could obtain the global optimal solution of EVD, and the solution process was not affected by the initial value and had good numerical stability. The method could accurately estimate the EVD and dynamic reliability of complex bridge structures under stochastic earthquakes. Both KDE and lognormal distribution failed to estimate the EVD of the structural seismic responses at small failure probability levels. It is thereby recommended that MEM is adopted for the seismic reliability analysis of bridge structures.