A　new　response　spectrum　method,　which　is　named　complex　multiple-support　response　spectrum　(CMSRS)　method　in　this　article,　is　developed　for　seismic　analysis　of　non-classically　damped　linear　system　subjected　to　spatially　varying　multiple-supported　ground　motion.　The　CMSRS　method　is　based　on　fundamental　principles　of　random　vibration　theory　and　properly　accounts　for　the　effect　of　correlation　between　the　support　motions　as　well　as　between　the　modal　displacement　and　velocity　responses　of　structure,　and　provides　an　reasonable　and　acceptable　estimate　of　the　peak　response　in　term　of　peak　seismic　ground　motions　and　response　spectra　at　the　support　points　and　the　coherency　function.　Meanwhile,　three　new　cross-correlation　coefficients　or　cross　covariance　especially　for　the　non-classically　damped　linear　structures　with　multiple-supports　excitations　are　derived　under　the　same　assumptions　of　the　MSRS　method　of　classically　damped　system.　The　CMSRS　method　is　examined　and　compared　to　the　results　of　time　history　analyses　in　two　numerical　examples　of　non-classically　damped　structures　in　consideration　of　the　coherences　of　spatially　variable　ground　motion.　The　results　show　that　for　non-classically　damped　structure,　the　cross　terms　representing　the　cross　covariance　between　the　pseudo-static　and　dynamic　component　are　also　quite　small　just　as　same　as　classically　damped　system.　In　addition,　it　is　found　that　the　usual　way　of　neglecting　all　the　off-diagonal　elements　in　transformed　damping　matrix　in　modal　coordinates　in　order　to　make　the　concerned　non-classically　damped　structure　to　become　remaining　proportional　damping　property　will　bring　some　errors　in　the　case　of　subjected　to　spatially　excited　inhomogeneous　ground　motion.