We have constructed a comprehensive grid of 1540 metal line-blanketed, NLTE, plane-parallel, hydrostatic model atmospheres for the basic parameters appropriate to early B-type stars. The BSTAR2006 grid considers 16 values of effective temperatures, 15,000 K<=Teff<=30,000 K with 1000 K steps, 13 surface gravities, 1.75<=logg<=4.75 with 0.25 dex steps, six chemical compositions, and a microturbulent velocity of 2 km s-1. The lower limit of logg for a given effective temperature is set by an approximate location of the Eddington limit. The selected chemical compositions range from twice to one-tenth of the solar metallicity and metal-free. Additional model atmospheres for B supergiants (logg<=3.0) have been calculated with a higher microturbulent velocity (10 km s-1) and a surface composition that is enriched in helium and nitrogen and depleted in carbon. This new grid complements our earlier OSTAR2002 grid of O-type stars (our Paper I). The paper contains a description of the BSTAR2006 grid and some illustrative examples and comparisons. NLTE ionization fractions, bolometric corrections, radiative accelerations, and effective gravities are obtained over the parameter range covered by the grid. By extrapolating radiative accelerations, we have determined an improved estimate of the Eddington limit in absence of rotation between 55,000 and 15,000 K. The complete BSTAR2006 grid is available at the TLUSTY Web site.