It　is　an　important　topic　to　improve　the　redundancy　of　optimized　configuration　to　resist　the　local　failure　in　topology　optimization　of　continuum　structures.　Such　a　fail-safe　topology　optimization　problem　has　been　solved　effectively　in　the　field　of　statics.　In　this　paper,　the　fail-safe　topology　optimization　problem　is　extended　to　the　field　of　frequency　topology　optimization.　Based　on　the　independent　continuous　mapping　(ICM)　method,　the　model　of　fail-safe　topology　optimization　is　established　with　the　objective　of　minimal　weight　integrating　with　the　discrete　condition　of　topological　variables　and　the　constraint　of　the　fundamental　frequency.　The　fail-safe　optimization　model　established　above　is　substituted　by　a　sequence　of　subproblems　in　the　form　of　the　quadratic　program　with　exact　second-order　information　and　solved　efficiently　by　the　dual　sequence　quadratic　programming　(DSQP)　algorithm.　The　numerical　result　reveals　that　the　optimized　fail-safe　structure　has　more　complex　configuration　and　preserved　materials　than　the　structure　obtained　from　the　traditional　frequency　topology　optimization,　which　means　that　the　optimized　fail-safe　structure　has　higher　redundancy.　Moreover,　the　optimized　fail-safe　structure　guarantees　that　the　natural　frequency　meets　the　constraint　of　fundamental　frequency　when　the　local　failure　occurs,　which　can　avoid　the　structural　frequency　to　be　sensitive　to　local　failure.　The　fail-safe　optimization　topology　model　is　proved　effective　and　feasible　by　four　numerical　examples.