Training automated trading agents is a long-standing topic that has been widely discussed in artificial intelligence for the quantitative finance. Reinforcement learning (RL) is designed to solve the sequential decision-making tasks, like the stock trading. The output of the RL is the policy which can be presented as the probability values of the possible actions based on a given state. The policy is optimized by the reward function. However, even if the profit is considered as the natural reward function, a trading agent equipped with an RL model has several serious problems. Specifically, profit is only obtained after executing sell action, different profits exist at the same time step due to the varying-length transactions and the hold action deals with two opposite states, empty or nonempty position. To alleviate these shortcomings, in this paper, we introduce a new trading action called wait for the empty position status and design the appropriate rewards to all actions. Based on the new action space and reward functions, a novel approach named Transaction-aware Inverse Reinforcement Learning (TAIRL) is proposed. TAIRL rewards all trading actions for avoiding the reward bias and dilemma. TAIRL is evaluated by backtesting on 12 stocks of US, UK and China stock markets, and compared against other state-of-art RL methods and moving average trading methods. The experimental results show that the agent of TAIRL achieves the state-of-art performance in profitability and anti-risk ability. Graphical abstract: [Figure not available: see fulltext.]