In　this　work,　we　investigate　linear　precoding　for　secure　spatial　modulation.　With　secure　spatial　modulation,　the　achievable　secrecy　rate　does　not　have　an　easy-to-compute　mathematical　expression,　and　hence,　has　to　be　evaluated　numerically,　which　leads　to　high　complexity　in　the　optimal　precoder　design.　To　address　this　issue,　an　accurate　and　analytical　approximation　of　the　secrecy　rate　is　derived　in　this　work.　Using　this　approximation　as　the　objective　function,　two　low-complexity　linear　precoding　methods　based　on　gradient　descent　(GD)　and　successive　convex　approximation　(SCA)　are　proposed.　The　GD-based　method　has　much　lower　complexity　but　usually　converges　to　a　local　optimum.　On　the　other　hand,　the　SCA-based　method　uses　semi-definite　relaxation　to　deal　with　the　non-convexity　in　the　precoder　optimization　problem　and　achieves　near-optimal　solution.　Compared　with　the　existing　GD-based　precoder　design　in　the　literature　that　directly　uses　the　exact　and　numerically　evaluated　secrecy　capacity　as　the　objective　function,　the　two　proposed　designs　have　significantly　lower　complexity.　Our　SCA-based　design　even　achieves　a　higher　secrecy　rate　than　the　existing　GD-based　design.　©　2020　Elsevier　B.V.