The　inverse　design　method　of　a　dynamic　system　with　linear　parameters　has　been　studied.　For　some　specified　eigenvalues　and　eigenvectors,　the　design　parameter　vector　which　is　often　composed　of　whole　or　part　of　coefficients　of　spring　and　mass　of　the　system　can　be　obtained　and　the　rigidity　and　mass　matrices　of　an　initially　designed　structure　can　be　reconstructed　through　solving　linear　algebra　equations.　By　using　implicit　function　theorem,　the　conditions　of　existence　and　uniqueness　of　the　solution　are　also　deduced.　The　theory　and　method　can　be　used　for　inverse　vibration　design　of　complex　structure　system.