Over the past decade, information for precision disease medicine has accumulated in the form of textual data. To effectively utilize this expanding medical text, we proposed a multi-task learning-based framework based on hard parameter sharing for knowledge graph construction (MKG), and then used it to automatically extract gastric cancer (GC)-related biomedical knowledge from the literature and identify GC drug candidates. In MKG, we designed three separate modules, MT-BGIPN, MT-SGTF and MT-ScBERT, for entity recognition, entity normalization, and relation classification, respectively. To address the challenges posed by the long and irregular naming of medical entities, the MT-BGIPN utilized bidirectional gated recurrent unit and interactive pointer network techniques, significantly improving entity recognition accuracy to an average F1 value of 84.5% across datasets. In MT-SGTF, we employed the term frequency-inverse document frequency and the gated attention unit. These combine both semantic and characteristic features of entities, resulting in an average Hits@1 score of 94.5% across five datasets. The MT-ScBERT integrated cross-text, entity, and context features, yielding an average F1 value of 86.9% across 11 relation classification datasets. Based on the MKG, we then developed a specific knowledge graph for GC (MKG-GC), which encompasses a total of 9,129 entities and 88,482 triplets. Lastly, the MKG-GC was used to predict potential GC drugs using a pre-trained language model called BioKGE-BERT and a drug-disease discriminant model based on CNN-BiLSTM. Remarkably, nine out of the top ten predicted drugs have been previously reported as effective for gastric cancer treatment. Finally, an online platform was created for exploration and visualization of MKG-GC at https://www.yanglab-mi.org.cn/MKG-GC/.