Dislocation behavior is a critical feature in describing the reliable properties of structures and materials. As a new kind of smart material, multiferroic solids have special applications on the coupling systems of mechanical, electric, and magnetic fields. Then, the moving dislocation in multiferroic solids has special interests for strength characteristics. In the present work, the moving edge dislocation is studied by the eigenstrain theory. The explicit solutions are derived and can be reduced to the piezoelectric and even pure elastic materials as the special cases.