We present the far-ultraviolet (FUV) fluorescent molecular hydrogen (H2) emission map of the Milky Way Galaxy obtained with FIMS/SPEAR covering ∼76% of the sky. The extinction-corrected intensity of the fluorescent H2 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 Hα emission. The all-sky H2 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 H2 (fH2) and the gas-to-dust ratio (GDR) of the diffuse ISM. The fH2 gradually increases from <1% at optically thin regions where E(B-V) < 0.1 to ∼50% for E (B-V) = 3. The estimated GDR is ∼5.1 × 1021 atoms cm -2 mag -1, in agreement with the standard value of 5.8 × 1021 atoms cm -2 mag -1.