Recently,　Transformer-based　models　have　shown　promising　results　in　automatic　speech　recognition　(ASR),　outperforming　models　based　on　recurrent　neural　networks　(RNNs)　and　convolutional　neural　networks　(CNNs).　However,　directly　applying　a　Transformer　to　the　ASR　task　does　not　exploit　the　correlation　among　speech　frames　effectively,　leaving　the　model　trapped　in　a　sub-optimal　solution.　To　this　end,　we　propose　a　local　attention　Transformer　model　for　speech　recognition　that　combines　the　high　correlation　among　speech　frames.　Specifically,　we　use　relative　positional　embedding,　rather　than　absolute　positional　embedding,　to　improve　the　generalization　of　the　Transformer　for　speech　sequences　of　different　lengths.　Secondly,　we　add　local　attention　based　on　parametric　positional　relations　to　the　self-attentive　module　and　explicitly　incorporate　prior　knowledge　into　the　self-attentive　module　to　make　the　training　process　insensitive　to　hyperparameters,　thus　improving　the　performance.　Experiments　carried　out　on　the　LibriSpeech　dataset　show　that　our　proposed　approach　achieves　a　word　error　rate　of　2.3/5.5%　by　language　model　fusion　without　any　external　data　and　reduces　the　word　error　rate　by　17.8/9.8%　compared　to　the　baseline.　The　results　are　also　close　to,　or　better　than,　other　state-of-the-art　end-to-end　models.