Triple-negative breast cancer (TNBC) is an aggressive malignant tumor with a high death rate in the whole world. This cancer mainly occurs in young women group possessed with poor prognoses. Long noncoding RNAs (lncRNAs) are known for regulating human diseases and cancers. Even though growing researches have illuminated that lncRNAs have a close relation with TNBC progression, the function of lncRNAPSMA3 antisense RNA 1 (PSMA3-AS1) in TNBC has not been discussed and exposed yet. In the present research, the expression pattern and functional role of PSMA3-AS1 were analyzed and unveiled with the help of RT-qPCR and functional assays. The findings demonstrated that PSMA3-AS1 was notably upregulated in TNBC cells. Silencing of PSMA3-AS1 had suppressing effects on TNBC cell growth and migration. Mechanistically, PSMA3-AS1 induced upregulation of proteasome activator subunit 3 (PSME3) by functioning as a miR-186-5p sponge. Furthermore, rescue assays certified that overexpression of PSME3 or inhibition of miR-186-5p could abrogate the inhibiting role of silenced PSMA3-AS1 on TNBC cell functions. To summarize, PSMA3-AS1 abolishes miR-186-5p-mediated suppression on PSME3 to accelerate TNBC progression.