Learning from interacting with environment and delayed reward are the two most important features of reinforcement learning. Because of these two characteristics, reinforcement learning is suitable for control problems. This thesis adopts reinforcement learning to establish several Taiwan stock index future intra-day trading strategies. We design three different definitions of state and use Q-learning and SARSA to implement reinforcement learning. In addition, we discuss the effect of setting maximum acceptable loss and minimum acceptable profit. To verify the usability of our strategies, we use real historical data for back testing and then examine the performance of the trading strategies.