In this paper, we adopt the time-multiplexed-superimposed training and investigate channel estimation for amplify-and-forward (AF) two-way relay network (TWRN) under doubly-selective channel scenario. With the aid of the complex-exponential basis-expansion-model (CE-BEM), we first develop the estimation model for BEM coefficient-vectors (BEM-CVs) of the individual channels between both sources and the relay. A two-step coarse estimator is proposed to obtain the BEM-CVs of the individual channels. Finally, numerical results are provided to corroborate the above studies.