The　transient　response　of　a　structure　is　usually　ignored　in　traditional　dynamic　analysis.　Based　on　the　theory　of　harmonic　earthquake　response　and　wavelet　packet　analysis,　the　transient　vibration　of　a　MDOF　system　subjected　to　real　earthquake　ground　motion　was　studied.　Response　spectra　and　transient　vibration　rules　of　the　equivalent　SDOF　system　were　analyzed.　It　was　concluded　that　the　maximum　displacement　of　a　long　period　structure　may　occur　in　transient　vibration　and　its　value　is　greater　than　its　resonance　displacement.　By　comparing　the　transient　response　of　a　long　period　building　with　that　of　a　short　period　one,　it　was　shown　that　short　period　structures　are　mainly　controlled　by　steady　state　vibration　and　the　effects　of　transient　vibration　on　a　long　period　structure　is　prominent.　Therefore,　transient　displacement　and　resonance　one　should　be　considered　in　earthquake-resistant　design　of　long　period　structures.