Short-term voltage stability is an increasing concern in today's power systems due to the growing penetration of induction motors. This paper proposes a systematic method for optimal placement of dynamic VAR support against short-term voltage instability. The problem is formulated as a multi-objective optimization model minimizing two conflicting objectives: 1) the total investment cost and 2) the expected unacceptable short-term voltage performance subject to a set of probable contingencies. STATCOM is employed for its stronger dynamic VAR support capability. Indices for quantifying the short-term voltage stability and the related risk level are proposed for problem modeling. Candidate buses are selected based on the concept of trajectory sensitivity. Load dynamics are fully considered using a composite load model containing induction motor and other typical components. A relatively new and superior multi-objective evolutionary algorithm called MOEA/D is introduced and employed to find the Pareto optimal solutions of the model. The proposed method is verified on the New England 39-bus system using industry-grade models and simulation tool.