The causation of edge distortion in conduction-cooled and end-pumped Nd∶YAG slab laser is analyzed and the experiment to suppress the slab edge distortion is conducted. The numerical simulation is done based on the experimental paramters indicating the result is consistent with the experimental one. The usage of the liquid epoxy-mucilage as heat conduction material to make a real-time cooling of the laser slab side can increase the energy ratio of fluorescence escaping from the laser slab side, which results in the reduction of the amplified spontaneous emission and the edge distortion peak-vallege value by 50%. This method possesses the advantage of enhancing the slab laser beam quality and output power.