B-type stars are known to rotate at various velocities, including very fast rotators near the critical velocity as the Be stars. In this paper, we provide stellar models covering the mass range between 1.7 to 15M_{sun}_, which includes the typical mass of known Be stars, at Z=0.014, 0.006 and 0.002 and for an extended range of initial velocities on the zero-age main sequence. We use the Geneva stellar-evolution code including the effects of shellular rotation and with a numerical treatment that has been improved in order for the code to track in a precise way the variation of the angular momentum content of the star as it changes under the influence of radiative winds and/or mechanical mass loss. We discuss the impact of the initial rotation rate on the tracks in the Hertzsprung-Russell diagram, the main-sequence (MS) lifetimes, the evolution of the surface rotation and abundances, as well as on the ejected masses of various isotopes. Among the new results obtained from the present grid we have that: 1) fast rotating stars with initial masses around 1.7M_{sun}_ present at the beginning of the core hydrogen-burning phase quite small convective cores with respect to their slowly rotating counterparts. This fact may be interesting to keep in mind in the frame of the asteroseismic studies of such stars; 2) the contrast between the core and surface angular velocity is higher in slower rotating stars. The values presently obtained are quite in the range of the very few values obtained for B-type stars from asteroseismology; 3) at Z=0.002, the stars in the mass range of 1.7 to 3M_{sun}_ with a mean velocity on the MS of the order of 150km/s show N/H enhancement superior to 0.2dex at mid-MS, and superior to 0.4dex at the end of the MS phase. At solar metallicity the corresponding values are below 0.2dex at any time in the MS. An extended database of stellar models containing 270 evolutionary tracks is provided to the community.