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We consider retrofitting structure-aware Transformer-based language model for facilitating end tasks by proposing to exploit syntactic distance to encode both the phrasal constituency and dependency connection into the language model. A middle-layer structural learning strategy is leveraged for structure integration, accomplished with main semantic task training under multi-task learning scheme. Experimental results show that the retrofitted structure-aware Transformer language model achieves improved perplexity, meanwhile inducing accurate syntactic phrases. By performing structure-aware fine-tuning, our model achieves significant improvements for both semantic- and syntactic-dependent tasks.