Abstract: Monolayer alpha-graphyne was recently proposed as a new all-carbon material having an electronic spectrum consisting of Dirac cones. Based on a first-principles investigation of bilayer alpha-graphyne, we show that the electronic band structure is qualitatively different from its monolayer form and depends crucially on the stacking mode of the two layers. Two stable stacking modes are found: a configuration with a gapless parabolic band structure, similar to AB stacked bilayer graphene, and another one which exhibits a doubled Dirac-cone spectrum. The latter can be tuned by an electric field with a gap opening rate of 0.3 eA. (C) 2013 AIP Publishing LLC.