A semi-definite programming (SDP) formulation of the multi-objective economic-emission dispatch problem is presented. The fuel cost and emission functions are represented by high order polynomial functions and this was shown to be a more accurate representation of the economic-emission dispatch (EED) problem. Furthermore, the polynomial functions of both objective functions are aggregated into a single objective function using the weighted sum approach. This thus reduces the problem to a standard polynomial optimization problem which was formulated as a hierarchy of semi-definite relaxation problems. The resulting SDP problem was then solved at different degrees of approximation. The performance of the proposed approach was evaluated by conducting experiments on the standard 6-unit and the 13-unit IEEE test systems. The results obtained were compared with those reported in the literature and indicated that SDP has inherently good convergence property and provides better exploration of the Pareto front.