In this paper, a secure spatial modulation (SM) system with artificial noise (AN)-aided is investigated. To achieve higher secrecy rate (SR) in such a system, two high-performance schemes of transmit antenna selection (TAS), leakage-based and maximum secrecy rate (Max-SR), are proposed and a generalized Euclidean distance-optimized antenna selection (EDAS) method is designed. From simulation results and analysis, the four TAS schemes have an decreasing order: Max-SR, leakage-based, generalized EDAS, and random (conventional), in terms of SR performance. However, the proposed Max-SR method requires the exhaustive search to achieve the optimal SR performance, thus its complexity is extremely high as the number of antennas tends to medium and large scale. The proposed leakage-based method approaches the Max-SR method with much lower complexity. Thus, it achieves a good balance between complexity and SR performance. In terms of bit error rate (BER), their performances are in an increasing order: random, leakage-based, Max-SR, and generalized EDAS.