Symbolic music generation is still an unsolved problem in the field of artificial intelligence and faces many challenges. It has been found that the existing methods for generating polyphonic music fail to meet the marke requirements in terms of melody， rhythm and harmony， and most of the generated music does not conform to basic music theory knowledge. In order to solve the above problems， a new Transformer-based multi-track music Generative Adversarial Network （Transformer-GAN） was proposed to generate music with high musicality under the guidance of music rules. Firstly， the decoding part of Transformer and the Cross-Track Transformer （CT-Transformer） adapted on the basis of Transformer were used to learn the information within a single track and between multiple tracks respectively. Then， a combination of music rules and cross-entropy loss was employed to guide the training of the generative network， and the well-designed objective loss function was optimized while training the discriminative network. Finally， multi-track music works with melody， rhythm and harmony were generated. Experimental results show that compared with other multi-instrument music generation models， for piano， guitar and bass tracks， Transformer-GAN improves Prediction Accuracy （PA） by a minimum of 12%， 11% and 22%， improves Sequence Similarity （SS） by a minimum of 13%， 6% and 10%， and improves the rest index by a minimum of 8%， 4% and 17%. It can be seen that Transformer -GAN can effectively improve the indicators including PA and SS of music after adding CT-Transformer and music rule reward module， which leads to a relatively high overall improvement of the generated music.