In this paper, a two-stage channel estimation scheme for two-way MIMO relay systems with a single relay antenna is proposed. The backward channel is estimated by using linear minimum mean square estimator (LMMSE) at the first stage, where the optimal training signal is designed. We then mainly focus on the forward channel estimation by using singular value decomposition (SVD) based maximum likelihood method, and the related training signal is proposed. We note that the forward channel estimator is nonlinear and by analyzing the asymptotic Bayesian Cramer-rao Lower Bound (BCRLB), we seek BCRLB as the criterion for training signal design. Finally, the numerical results show that the proposed training signal can improve the MSE performance.