An explicit time-domain method(ETDM) based on analytical response of unit impulse was proposed  to simulate the random seismic analysis of artificial seismic waves and building structures with response spectrum consistent with “Code for Seismic Design of Buildings” (GB 50011—2010). Firstly, explicit time domain expressions based on analytical response of unit impulse for single and multiple degree of freedom dynamical systems were derived. Then, the explicit time domain expression for single degree of freedom system was applied to solve the stochastic dynamic equation of the ground motion. Through iteration, the artificial seismic wave of the specified intensity and the artificial seismic wave that is consistent with the standard response spectrum can be simulated efficiently by taking the advantage of equation in quickly solving the dynamic response. Then, the explicit time-domain expressions of the simulated seismic wave and the multi-degree-of-freedom dynamic system were applied to the random seismic simulation analysis of structures and verified by a numerical example. The study shows that, based on the existing ground motion model and the explicit time domain representation of the unit pulse, the seismic wave which is consistent with the standard response spectrum can be simulated efficiently, and ETDM based on unit pulse combined with mode superposition method has sufficient accuracy and high efficiency in seismic random simulation analysis of structures, thus can be used for seismic time-history analysis of building structures.