HDAC1 functions as an oncogene in multi-type cancers. This study aimed to investigate the roles of histone deacetylase 1 (HDAC1) in cervical cancer (CC). mRNA expression was determined using reverse transcription quantitative polymerase chain reaction. The protein-protein complexes was analyzed using co-immunoprecipitation assay. The binding sites between NRF2 and NEU1 were confirmed by chromatin immunoprecipitation assay. Cell viability was detected by CCK-8. Cell proliferation was measured using CCK-8 and colony formation assays. Cell migrative and invasive ability were determined using transwell assay. We found that HDAC1 was upregulated in CC patients and cells. Trichostatin A (TSA) treatment decreased the number of colonies and migrated and invaded cells. Moreover, HDAC1 interacted with NRF2 to downregulate NEU1 expression. NEU1 knockdown attenuated the effects of TSA and enhanced the aggressiveness of CC cells. In conclusion, HDAC1 functions as an oncogene in CC. Targeting HDAC1 may be an alternative strategy for CC.