Dissemination of multidrug-resistant, particularly tigecycline-resistant, Acinetobacter baumannii is of critical importance, as tigecycline is considered a last-line antibiotic. Acquisition of tet(X), a tigecycline-inactivating enzyme mostly found in strains of animal origin, imparts tigecycline resistance to A. baumannii. Herein, we investigated the presence of tet(X) variants among 228 tigecycline-non-susceptible A. baumannii isolates from patients at a Taiwanese hospital via polymerase chain reaction using a newly designed universal primer pair. Seven strains (3%) carrying tet(X)-like genes were subjected to whole genome sequencing, revealing high DNA identity. Phylogenetic analysis based on the PFGE profile clustered the seven strains in a clade, which were thus considered outbreak strains. These strains, which were found to co-harbor the chromosome-encoded tet(X6) and the plasmid-encoded bla_OXA-72 genes, showed a distinct genotype with an uncommon sequence type (Oxford ST793/Pasteur ST723) and a new capsular type (KL129). In conclusion, we identified an outbreak clone co-carrying tet(X6) and bla_OXA-72 among a group of clinical A. baumannii isolates in Taiwan. To the best of our knowledge, this is the first description of tet(X6) in humans and the first report of a tet(X)-like gene in Taiwan. These findings identify the risk for the spread of tet(X6)-carrying tigecycline- and carbapenem-resistant A. baumannii in human healthcare settings.