A　random　vibration　study　of　structures　under　multi-component　seismic　excitations　is　presented　in　this　paper.　The　pseudo　excitation　method　proposed　by　J.　H.　Lin　is　employed　and　is　further　developed,　from　which　a　multi-component　pseudo　excitation　method　is　formulated.　Then,　the　random　model　and　correlation　for　multiple　ground　motions　are　investigated.　Based　on　the　method,　a　computer　program　is　developed　and　a　random　vibration　study　is　performed　for　a　double-layer　spherical　lattice　shell　to　investigate　its　seismic　performance　under　multi-component　seismic　excitations.　It　is　found　that　a　significant　difference　may　occur　between　single　and　multi-component　seismic　excitations.　The　present　study　has　shown　that　the　developed　method　is　a　highly　efficient　and　accurate　CQC　algorithm,　in　which　all　the　cross-correlation　terms　between　both　participant　modes　and　seismic　excitations　are　involved.　This　method　can　easily　be　used　for　multi-component　seismic　analysis　of　structures　that　have　closely　spaced　natural　frequencies　and　coupled　vibration　modes.