Abstract: A real value form formula of complex mode response superposition method,which is based on the stationary random vibration theory and seismic design spectra,is derived to analysis the non-classically damped linear system.This formula includes new modal velocity correlation coefficient and displacement-velocity cross correlation coefficients besides the modal displacement correlation coefficient in normal Complete Quadratic Combination(CQC) formula.Moreover,the new method has same accuracy and concision as normal CQC method because there is no further assumption involved in it except that have been adopted in normal CQC method.The new proposed CCQC method is easy to master and apply for design engineers.The example analyses and the numerical comparisons with CCQC method,CSRSS method,and the forced uncoupling method proposed by seismic design code are carried out.The results are verified by those obtained from the step-by-step integration method under the simulated man-made seismic wave input.The results demonstrated that CCQC method based on design spectra is more accurate than CSRSS method.Meanwhile,the forced mode uncoupling method widely used in seismic design code also has good approximation,even though the relatively simple example structure is strongly non-proportional.