This　paper　presents　a　trigonometric　series　method　to　synthesize　simulated　earthquake　waves.　In　this　method,　theoretical　and　numerical　solutions　are　combined　to　calculate　the　contribution　of　each　frequency　component　to　response　spectrum　used　for　amplitude　spectrum　correction　to　reduce　numerical　errors　in　solving　simple　harmonic　motions　with　periods　close　to　the　numerical　time　step.　Least　square　method　is　used　to　regulate　earthquake　waves　generated　in　the　iterative　process,　and　the　corrected　standard　earthquake　waves　are　normalized.　The　method　can　ensure　the　accuracy　of　amplitude　spectrum　adjustment　and　improve　numerical　stability　and　convergence　in　the　iteration　of　simulated　earthquake　wave　computation.　Application　of　the　method　to　the　concrete　faced　rockfill　dam　of　Fujian　Xianyou　pumped　storage　power　station　shows　that　the　synthesized　earthquake　waves　meets　the　accuracy　requirement　of　response　spectrum　in　hydraulic　structure　design　and　the　design　requirement　of　peak　acceleration,　while　eliminating　the　shifts　in　time　developments　of　velocity　and　displacement　of　the　simulated　earthquake　waves.　©　Copyright.