Graphdiyne, consisting of sp- and sp(2)-hybridized carbon atoms, is a new member of carbon allotropes which has a natural band gap similar to 1.0 eV. Here, we report our first-principles calculations on the stable configurations and electronic structures of graphdiyne doped with boron-nitrogen (BN) units. We show that BN unit prefers to replace the sp-hybridized carbon atoms in the chain at a low doping rate, forming linear BN atomic chains between carbon hexagons. At a high doping rate, BN units replace first the carbon atoms in the hexagons and then those in the chains. A comparison study indicates that these substitution reactions may be easier to occur than those on graphene which composes purely of sp(2)-hybridized carbon atoms. With the increase of BN component, the band gap increases first gradually and then abruptly, corresponding to the transition between the two substitution motifs. The direct-band gap feature is intact in these BN-doped graphdiyne regardless the doping rate. A simple tight-binding model is proposed to interpret the origin of the band gap opening behaviors. Such wide-range band gap modification in graphdiyne may find applications in nanoscaled electronic devices and solar cells.