In this paper, we propose general-order transmit antenna selection to enhance the secrecy performance of multipleinput multiple-output multi-eavesdropper channels with the outdated channel state information (CSI) at the transmitter. To evaluate the effect of outdated CSI on the secure transmission of the system, we investigate the secrecy performance for two practical scenarios, i.e., Scenario I: the eavesdropper's CSI is not available at the transmitter, and Scenario II: the eavesdropper's CSI is available at the transmitter. For Scenario I, we derive exact and asymptotic closed-form expressions for the secrecy outage probability in Nakagami-m fading channels. In addition, we also derive the probability of non-zero secrecy capacity and the ε-outage secrecy capacity, respectively. Simple asymptotic expressions for the secrecy outage probability reveal that the secrecy diversity order is reduced when CSI is outdated at the transmitter, and is independent of the number of antennas at each eavesdropper NE, fading parameter of the eavesdropper's channel mE, and the number of eavesdroppers M . For Scenario II, we make a comprehensive analysis of the average secrecy capacity obtained by the system. Specifically, new closed-form expressions for the exact and asymptotic average secrecy capacity are derived, which are valid for general systems with arbitrary number of antennas, number of eavesdroppers and fading severity parameters. Resorting to these results, we also determine the high signal-to-noise ratio power offset to explicitly quantify the impacts of the main channel and the eavesdropper's channel on the average secrecy capacity.Index Terms-MIMO wiretap channel, physical layer security, transmit antenna selection, Nakagami-m fading.