In recent years, with the advance of Artificial Intelligence, automatic music composition has been demonstrated. However, there are many music genres and music instruments. For a same piece of music, different music instruments would produce different effects. Invented some 2500 years ago, Guzheng is one of the oldest music instruments in China and the world. It has distinct timbres and patterns that cannot be duplicated by other music instruments. Therefore, it is interesting to see whether AI can compose Guzheng music or alike. In this paper we present a method that can automatically compose and play Guzheng music. First, we collect a number of existing Guzheng music pieces and convert them into Music Instrument Digital Interface format. Second, we use these data to train a Long Short-Term Memory (LSTM) network and use the trained network to generate new Guzheng music pieces. Next, we use the Reinforcement Learning to optimize the LSTM network by adding special Guzheng playing techniques. Comparing to the existing AI methods, such as LSTM and Generative Adversary Network, our new method is more effective in capturing the characteristics of Guzheng music. According to the evaluations from skilled Guzheng players and general audiences, our Guzheng music is very close to the real Guzheng music. The presented method can also be used to automatically compose the music of other Chinese music instruments.