This is the second paper of a series devoted to presenting an updated release of the BaSTI (a Bag of Stellar Tracks and Isochrones) stellar model and isochrone library. Following the publication of the updated solar-scaled library, here we present the library for an α-enhanced heavy element distribution. These new α-enhanced models account for all improvements and updates in the reference solar metal distribution and physics inputs, as in the new solar-scaled library. The models cover a mass range between 0.1 and 15 M⊙, 18 metallicities between [Fe/H] = -3.20 and +0.06 with [α/Fe] = +0.4, and a He-to-metal enrichment ratio ΔY/ΔZ = 1.31. For each metallicity, He-enhanced stellar models are also provided. The isochrones cover (typically) an age range between 20 Myr and 14.5 Gyr, including consistently the pre-main-sequence phase. The asteroseismic properties of the theoretical models have also been calculated. Models and isochrones have been compared with results from independent calculations, with the previous BaSTI release, and also with selected observations, to test the accuracy/reliability of these new calculations. All stellar evolution tracks, asteroseismic properties, and isochrones are publicly available at http://basti-iac.oa-teramo.inaf.it.