A monomolecular crystalline layer of "1,4,5,8-naphthalene-tetracarboxylic-dianhydride" (NTCDA) on a highly oriented pyrolytic graphite (HOPG) substrate was formed by vacuum deposition. By estimating molecular packing in a crystal by scanning tunneling microscopy, a new structure of the monolayer was suggested, which is different from those reported previously. Molecules were observed to be standing perpendicular to the HOPG surface and packed in a face-to-face manner. A thermal desorption process was observed in the monomolecular layer by temperature-variable atomic force microscopy (AFM). The in situ AFM observation clarified that NTCDA molecules desorbed from the edges of crystals just above room temperature. Morphological changes at a constant temperature of 308 K were observed in detail, where desorption rates were concluded to be anisotropically dependent on crystalline edges. This dependency originated from the anisotropy of intermolecular interaction. The rate order of the desorption process, a kinetic parameter, was evaluated to be 0.2, which corresponds well to the desorption behavior observed by AFM.