In this paper, we investigate the interference exploitation precoding for multi-level modulations in the downlink multi-antenna systems. We mathematically derive the optimal precoding structures based on the Karush-Kuhn-Tucker (KKT) conditions. Furthermore, by formulating the dual problem, the precoding problem for multi-level modulations can be transformed into a pre-scaling operation using quadratic programming (QP) optimization. Compared to the original second-order cone programming (SOCP) formulation, this transformation that finally leads to a QP optimization allows a considerable complexity reduction. Simulation results validate our derivations on the optimal precoding structure, and demonstrate significant performance improvements for interference exploitation precoding over traditional precoding methods for multi-level modulations.