Pre-trained natural language processing models on a large natural language corpus can naturally transfer learned knowledge to protein domains by fine-tuning specific in-domain tasks. However, few studies focused on enriching such protein language models by jointly learning protein properties from strongly-correlated protein tasks. Here we elaborately designed a multi-task learning (MTL) architecture, aiming to decipher implicit structural and evolutionary information from three sequence-level classification tasks for protein family, superfamily and fold. Considering the co-existing contextual relevance between human words and protein language, we employed BERT, pre-trained on a large natural language corpus, as our backbone to handle protein sequences. More importantly, the encoded knowledge obtained in the MTL stage can be well transferred to more fine-grained downstream tasks of TAPE. Experiments on structure- or evolution-related applications demonstrate that our approach outperforms many state-of-the-art Transformer-based protein models, especially in remote homology detection.