The seismic performance spectrum is a new kind of the response spectra which is formed according to the designated performance objectives. The performance objectives are changed according to the performance objective level and period of structure, and are different in the acceleration sensitive, velocity sensitive and displacement sensitive range in the seismic performance spectrum. The seismic performance spectrum formulas are derived, which demonstrate the mathematic relationship between the seismic demands of the different performance objective levels and the period of structure. The fitted formulas of the seismic performance spectra for seismic design are obtained due to statistical result of 1085 ground motion records. The new seismic performance spectra are shown in visual three-dimension figures which can represent the seismic demand, performance objective and period of structure in this paper. The philosophy of the seismic performance spectrum is analyzed which reveals the rules for estimating seismic demand of structure at the different performance objective levels. So the multi-objective performance-based seismic design is also proposed using the seismic performance spectrum.