As a Japanese National space mission with international collaboration, Solar-B (2005 launch) will carry a spectro- polarimeter (SP) to be operated in visible light to obtain the first high angular resolution, precision measurements of solar vector magnetic fields from space. The SP is part of the Focal Plane Package (FPP) fed by a diffraction-limited 50-cm optical telescope. The SP will be operated exclusively at the photospheric 630 nm Fe I lines. It features a rotating, low-order crystalline quartz retarder for polarization modulation and a reflecting Littrow spectrograph design that is shortened by using diffraction from the 12micrometers wide slit to fill the grating. Polarization analysis is accomplished by a modified Savart plate beam splitter. A custom CCD detector with two active areas, one for each beam from the beam splitter, allows continuous high duty-cycle sampling of polarization. The spectrograph slit will sample a 0.16 x 164 arcsec2 rectangle of the solar image, which may be scanned across the slit by up to +/- 160 arcsec in order to build up vector magnetic field maps of the solar photosphere. Along with simultaneous, co-spatial imaging and polarimetry with the filter imagers of the FPP, the SP will provide a precise view of active and quiet solar magnetic fields that control the structure, dynamics, and energetics of the upper solar atmosphere.