There are provided an apparatus and method for measuring thermal conductivity capable of easily and accurately obtaining an extent of thermal damage of a targeted tissue. The apparatus for measuring thermal conductivity in burns includes a thermal paper stacking member having a plurality of sheets of thermal paper stacked thereon to form layers, and a pressing member configured to press the stacking member so that the thermal paper is stacked and maintained in a closely adhered state. Here, an extent of thermal damage of the targeted tissue according to the depth can be calculated as an extent of thermal damage of the stacking member according to the depth.