In the realm of engineering structures, the distribution of structural parameters often remains uncertain due to a lack of sufficient data, presenting a common and intricate challenge in structural reliability analysis. This paper presents a novel linear moment method for assessing the seismic reliability of random structures with unknown distributions. A random dynamic system is constructed using only two basic random variables: (1) the first four-order linear moments derived from the structural random parameters, expressed as a univariate cubic polynomial with a random function involving standard normal random variables; (2) A random function-spectral representation model is utilized to describe the non-stationary seismic ground motion. On this basis, representative point sets for the two basic random variables are determined using number-theoretical methods. Through time-domain analysis, extreme structural responses are computed to evaluate the samples of the performance function and its linear moments within the specified limit state. The seismic reliability index derived from linear moments is established by solving the univariate cubic equation roots. To demonstrate the proposed method’s applicability, a nonlinear single-degree-of-freedom system with unknown parameter distributions is analyzed, and its effectiveness is verified by comparing the results with those obtained using Monte Carlo simulation.