We present the far-ultraviolet (FUV) fluorescent molecular hydrogen (H-2) emission map of the Milky Way Galaxy obtained with FIMS/SPEAR covering similar to 76% of the sky. The extinction-corrected intensity of the fluorescent H-2 emission has a strong linear correlation with the well-known tracers of the cold interstellar medium (ISM), including color excess E(B-V), neutral hydrogen column density N(H I), and H alpha emission. The all-sky H-2 column density map was also obtained using a simple photodissociation region model and interstellar radiation fields derived from UV star catalogs. We estimated the fraction of H-2 (f(H2)) and the gas-to-dust ratio (GDR) of the diffuse ISM. The f(H2) gradually increases from <1% at optically thin regions where E(B-V) <0.1 to similar to 50% for E (B-V) = 3. The estimated GDR is similar to 5.1 x 10(21) atoms cm(-2) mag(-1), in agreement with the standard value of 5.8 x 10(21) atoms cm(-2) mag(-1).