Abstract: How to determine the structural seismic demands up to the displacement-objective is one of the key tasks for performance-based seismic design. The displacement objectives are studied, the displacement objective parameters are determined and the relations between displacement-objectives and periods of single-degree-of-freedom systems are derived. The displacements of different periods are obtained by dynamic elastic-plastic differential equations of single-degree-of-freedom systems under 1085 ground motions. The displacements are adjusted up to the displacement-objectives by zooming ground motions. This paper acquires the functional relations among seismic demands, structural period and performance objectives, establishes the statistical performance spectra under a three-dimensional coordinate system and fits the empirical formulas of performance spectra. The results show that the performance spectra function is an effective method, which determine the seismic demands under different performance objectives. The performance spectra curves decrease with the increasing periods obviously and increase with the increasing performance objectives gradually. The performance spectra have no horizontal section, the resonance effect of the sites disappears and the sites do not obviously affect the performance spectra. The seismic demand inferences up to the performance objectives and the seismic performance assessments can use the fitting formulas.