In this paper, with the help of an intelligent reflecting surface (IRS), the source (S) and destination (D) exchange information through the two-way decode-and-forward relay (TW-DFR). We mainly focus on the phase optimization of IRS to improve the system rate performance. Firstly, a maximizing receive power sum (Max-RPS) method is proposed via eigenvalue decomposition (EVD) with an appreciable rate enhancement, which is called Max-RPS-EVD. To further achieve a higher rate, a method of maximizing minimum rate (Max-Min-R) is proposed with high complexity. To reduce its complexity, a low-complexity method of maximizing the sum rate (Max-SR) via general power iterative (GPI) is proposed, which is called Max-SR-GPI. Simulation results show that the proposed three methods outperform the case of random phase method, especially the proposed Max-SR-GPI method is the best one achieving at least 20\% rate gain over random phase. Additionally, it is also proved the optimal rate can be achieved when TW-DFR and IRS are located in the middle of S and D.