In this study, an explicit time integration scheme based on cubic B-spline interpolation strategy and momentum corrector is extended for structural seismic response analysis. The acquisition strategy for the required seismic load is provided. The cubic B-spline-based scheme with moment corrector is generalized for the nonlinear hysteresis system. The analysis shows that the explicit scheme has more desirable stability and accuracy properties than other competitive schemes. The effectiveness of the scheme is demonstrated by the linear and nonlinear numerical examples.