Biomedical　semantic　indexing　refers　to　annotating　biomedical　citations　with　Medical　Subject　Headings,　which　is　crucial　for　texting　mining,　information　retrieval　and　other　researches　in　the　field　of　bioinformatics.　The　traditional　methods　ignore　the　relations　among　labels　and　need　complicated　feature　engineering.　In　this　paper,　we　present　a　novel　model　with　a　deep　serial　multi-task　learning　structure,　in　which　the　semantic　word　embedding　and　bidirectional　Gated　Recurrent　Unit　are　integrated　in　a　multi-task　learning　paradigm.　It　differs　from　an　ordinary　multi-task　structure　in　that　the　tasks　in　our　model　are　serial　and　tightly　coupled　rather　than　parallel.　The　dataset　of　the　2017　BioASQ-Task5A　is　used　to　evaluate　the　performance.　Without　any　handcrafted　feature,　our　model　outperforms　MTI,　the　state-of-the-art　solution　proposed　by　the　US　National　Library　of　Medicine.　It　also　achieves　the　highest　precision　among　all　the　solutions　in　2017　BioASQ-Task5A,　and　converges　faster　than　some　naive　deep　learning　methods.