This paper studies the secrecy performance of multiple-input multiple-output (MIMO) wiretap channels, also termed as multiple-input multiple-output multiple-eavesdropper (MIMOME) channels, under transmit antenna selection (TAS) and BPSK/QPSK modulations. In the main channel between the transmitter and the legitimate receiver, a single transmit antenna is selected to maximizes the instantaneous Signal to Noise Ratio (SNR) at the receiver. At the receiver and the eavesdropper, selection combination (SC) is utilized. By assuming Rayleigh flat fading, we first derive the closed-form approximated expression for the ergodic secrecy rate when the channel state information of the eavesdropper (CSIE) is available at the transmitter. Next, analytical formulas for the approximated and asymptotic secrecy outage probability (SOP) are also developed when CSIE is unavailable. Besides theoretical derivations, simulation results are provided to demonstrate the approximation precision of the derived results. Furthermore, the asymptotic results reveal that the secrecy diversity order degrades into 0 due to the finitealphabet inputs, which is totally different from that driven by the Gaussian inputs.