The effects of single C-chain on the stability, structural and electronic properties of zigzag BN nanoribbons (ZBNNRs) were investigated by first-principles calculations. C-chain was expected to dope at B-edge for all the ribbon widths Nz considered. The band gaps of C-chain doped Nz-ZBNNR are narrower than that of perfect ZBNNR due to new localized states induced by C-chain. The band gaps of Nz-ZBNNR-C(n) are direct except for the case of C-chain position n=2. Band gaps of BN nanoribbons are tunable by C-chain and its position n, which may endow the potential applications of BNNR in electronics.