Abstract The effects of a single C-chain on the structural and electronic properties of the H terminated zigzag AlN nanoribbons (ZAlNNRs) have been investigated systemically by using the first-principles. The results show that in perfect 7-ZAlNNR for example, the states of the lowest unoccupied conduction band (LUCB) and the highest occupied valence band (HOVB) at zone boundary Z are edge states their charges are localized at edge Al and N atoms, respectively. Introducing a single C-chain and changing its position lead to the LUCB and HOVB getting closer with each other. Similar to the edge states existing in perfect ZAlNNR, the flat dispersion border states also exist in a single C-chain decorated ZAlNNR, but their charges are localized at border C–N and C–Al for LUCB and HOVB, respectively. Furthermore, for N z -ZAlNNR-C( n) with ribbon width N z = 2, 3, 4, 5, 6, 7 and 10, only N z -ZAlNNR-C(1) has a direct band gap, while the other N z -ZAlNNR-C( n) has an indirect band gap. Variation of the band gap with C-chain position n shows that, for N z -ZAlNNR-C( n) of arbitrary width N z , the N z -ZAlNNR-C(1) and N z -ZAlNNR-C(2) have nearly identical the minimum band gap of 0.132 eV and nearly identical the maximum band gap of 1 eV, respectively, except the maximum band gap of 0.63 eV for 2-ZAlNNR-C(2) because it belongs to the group of C-chain substituting the right edge Al–N chain, the band gap of this group decreases linearly with increasing ribbon width N z . For 3-, 4-, 5-, 6-, 7- and 10-ZAlNNR-C( n), the band gap decreases successively for C-chain position n from 2 to 3, 4, 5, 6, 7 and 10, respectively.