The　authors　put　forward　a　method　that　takes　the　response　spectrum　and　the　enveloping　curve　as　the　double　target　functions　to　synthesize　the　artificial　ground　motion.　The　method　not　only　makes　the　response　spectrum　of　the　artificial　ground　motion　comply　with　the　target　spectrum,　but　also　in　the　iterative　process　adjusts　the　ground　motion　wave-shape　to　conform　to　the　goal　enveloping　curve　function　approximately,　and　eliminates　the　base-line　shift　in　the　acceleration　time　history,　then　makes　the　velocity　and　displacement　time　histories　of　ground　motion　more　reasonable.　The　authors　argue　that　it　may　be　necessary　to　make　the　artificial　ground　motions　accord　with　both　the　target　response　spectrum　and　the　target　enveloping　function,　when　the　dynamic　response　characteristics　of　certain　nonlinear　structural　system　are　studied.