For　non-classically　damped　linear　system　with　over-critically　damping　peculiarity,　how　to　solve　the　seismic　response　by　using　complex　mode　superposition　technology　is　still　a　problem,　and　none　of　the　sufficient　research　is　available.　Starting　from　general　solution　based　on　the　complex　mode　superposition　algorithm,　a　mode　superposition　formula　in　time　domain　for　seismic　response　of　non-classically　damped　linear　system　is　deduced　in　this　paper.　Furthermore,　the　complex　complete　quadratic　combination　(CCQC)　formula,　and　the　complex　square　root　of　sum　of　squares　(CSRSS)　method　for　calculating　maximum　seismic　responses　on　the　base　of　design　spectra　are　also　provided.　The　correctness　and　effectiveness　of　these　formulas　are　verified　by　example.　The　basic　characteristics　of　the　non-classically　damped　linear　system　with　over-critical　damping　ratios,　the　numerical　integration　method　of　seismic　response　and　the　response　spectra-based　method　for　calculating　peak　response　are　described　in　detail　in　this　paper.　The　results　showed　that　the　complex　mode　superposition　algorithm　derived　from　general　linear　dynamic　system　with　complex　eigenvalues　and　eigenvectors　is　applicable　to　the　system　with　over-critical　damping　peculiarity　in　principle.　The　numerical　example　also　showed　that　the　forced　uncoupling　approach,　which　is　popularly　used　in　seismic　design　code,　is　likely　to　result　in　fairly　large　errors　when　over-critical　damping　ratios　present　partly　in　the　mode　shapes　of　non-classically　damped　linear　systems.