An electroosmotic ink printer head comprising a dielectric support having a surface defined by longitudinal front and rear edges and a pair of transverse edges. A plurality of first electrodes is successively arranged on said surface extending rearward from the front side of the support. A porous member is provided to overlie the first electrodes in contact with said surface. On the porous member is a second, liquid-permeable electrode on which is provided a means for supplying ink thereto to allow it to permeate therethrough to the porous member. A third electrode is located adjacent to each outermost one of the first electrodes and to the longitudinal front edge. A potential is applied to the third electrode with respect to the second electrode to cause the ink in the porous member to electroosmotically move in a direction from the third electrode to the second electrode. The ink which might wet the front edge of the support is pulled rearward by the electroosmotic movement.