Given　a　set　of　labels,　multi-label　text　classification　(MLTC)　aims　to　assign　multiple　relevant　labels　for　a　text.　Recently,　deep　learning　models　get　inspiring　results　in　MLTC.　Training　a　high-quality　deep　MLTC　model　typically　demands　large-scale　labeled　data.　And　comparing　with　annotations　for　single-label　data　samples,　annotations　for　multi-label　samples　are　typically　more　time-consuming　and　expensive.　Active　learning　can　enable　a　classification　model　to　achieve　optimal　prediction　performance　using　fewer　labeled　samples.　Although　active　learning　has　been　considered　for　deep　learning　models,　there　are　few　studies　on　active　learning　for　deep　multi-label　classification　models.　In　this　work,　for　the　deep　MLTC　model,　we　propose　a　deep　Active　Learning　method　based　on　Bayesian　deep　learning　and　Expected　confidence　(BEAL).　It　adopts　Bayesian　deep　learning　to　derive　the　deep　model＇s　posterior　predictive　distribution　and　defines　a　new　expected　confidence-based　acquisition　function　to　select　uncertain　samples　for　deep　MLTC　model　training.　Moreover,　we　perform　experiments　with　a　BERT-based　MLTC　model,　where　BERT　can　achieve　satisfactory　performance　by　fine-tuning　in　various　classification　tasks.　The　results　on　benchmark　datasets　demonstrate　that　BEAL　enables　more　efficient　model　training,　allowing　the　deep　model　to　achieve　training　convergence　with　fewer　labeled　samples.