To　efficiently　and　accurately　separate　sources　from　the　measured　signals　and　align　their　permutation,　a　convolutive　blind　source　separation　(BSS)　in　frequency　domain　with　kurtosis　maximization　(CBSS_FDKM)　by　the　modified　conjugate　gradient　is　proposed.　Firstly,　Short　Time　Fourier　Transform　(STFT)　is　used　to　convert　the　convolutive　BSS　problem　in　time　domain　into　an　instantaneous　BSS　in　frequency　domain.　Secondly,　CBSS_FDKM　is　adopted　to　separate　complex　signals　in　each　frequency　bin,　and　kurtosis　maximization　is　used　as　the　objective　function　and　optimized　by　a　modified　conjugate　gradient　with　iterative　step　sizes　optimized　by　an　efficient　algebraic　method,　and　thus　the　accuracy　and　convergence　speeds　are　significantly　enhanced.　Thirdly,　the　power　spectra　are　obtained　from　the　separated　signals　and　the　cosine　distances　based　on　power　spectra　are　calculated　for　permutation　alignment.　Finally,　inverse　Short　Time　Fourier　Transform　(ISTFT)　is　adopted　to　reconstruct　the　separated　signals　in　time　domain.　Furthermore,　the　accuracy　and　robustness　of　the　proposed　method　are　comparatively　studied　according　to　typical　numerical　studies　and　experimental　studies　on　a　cylindrical　test　bed.　Generally,　this　paper　provides　a　more　accurate　and　robust　BSS　for　source　separation　and　identification,　which　can　provide　significant　evidences　for　vibration　&　noise　monitoring　and　control.　(C)　2019　Published　by　Elsevier　Ltd.