The emission function associated with the economic-emission dispatch prob- lem contains exponential functions that model the emission pollutants. This paper presents a strategy of solving the economic-emission dispatch problem whereby the ex- ponential function is approximated by a rational function that permits reduction to a standard polynomial optimization problem. This is reformulated as a hierarchy of semidefinite relaxation problems using the moment theory and the resulting SDP prob- lem is solved. Different degrees of rational functional approximation were considered. The approach was tested on the IEEE 30-bus test systems to investigate its effectiveness. Solutions obtained were compared with those from some of the well known evolutionary methods. Results showed that SDP has inherently good convergence property and a lower but comparable diversity property.