We investigate the performance of multi-antenna two-way relay networks, where both amplify-and-forward (AF) and decode-and-forward (DF) relaying strategies are considered. First an antenna selection scheme among all nodes is proposed based on maximizing the worse received signal-to-noise ratio (SNR) of two end users. Then, we derive the probability density function (PDF) and cumulative distribution function (CDF) of the received SNRs of both users. We also obtain the closed-form expressions of average bit error rates (BER) and the outage probability of our system. Furthermore, we study the asymptotic behavior of our system when transmitting SNR or the number of antennas is large. The results show that the proposed antenna selection scheme achieves full diversity, and the simulation results closely match to our theoretical analysis. To further improve the spectrum efficiency of the system, a hybrid selection antenna scheme is proposed. Finally, the numerical results show that our scheme outperforms the state of art.