Diffuse far-ultraviolet (FUV; 1370 - 1670 angstrom) flux from the Taurus molecular cloud region has been observed with the SPEAR/FIMS imaging spectrograph. An FUV continuum map of the Taurus region, similar to the visual extinction maps, shows a distinct cloud core and halo region. The dense cloud core, where the visual extinction A(v) > 1.5, obscures the background diffuse FUV radiation, while scattered FUV radiation is seen in and beyond the halo region, where A(v) < 1.5. The total intensity of H-2 fluorescence in the cloud halo is I-H2 = 6.5 x 10(4) photons cm(-2) s(-1) sr(-1) in the 1370 - 1670 angstrom wavelength band. A synthetic model of the H-2 fluorescent emission fits the present observation best with a hydrogen density n(H) = 50 cm(-3), H-2 column density N(H-2) = 0.8 x 10(20) cm(-2), and incident FUV intensity I-UV = 0.2. H-2 fluorescence is not seen in the core, presumably because the required radiation flux to induce fluorescence is unable to penetrate the core region.