The present invention relates to a series of techniques for treating a waste material of an asbestos-containing material, from emergency treatment, dismantling, or transportation of an already constructed asbestos-containing material to a heating and melting treatment of the dismantled asbestos-containing waste material. The preset invention provides a method of preventing the exposure of the fibrous dust of the asbestos involving melting an asbestos-containing waste material, into which lithium silicate is impregnated in a melting furnace for treating an asbestos-containing material into harmless. The lithium silicate impregnated into the asbestos-containing waste material forms a gel within the range of temperatures of 500 to 1,100° C., and the formed gel adheres onto the surfaces of asbestos fibers, thereby preventing the exposure of the fibrous dust of the asbestos. Moreover, the melting temperature of asbestos can be reduced to about 1,360° C.