The two-dimensional (2D) C₃N has emerged as a material with promising applications in high performance device owing to its intrinsic bandgap and tunable electronic properties. Although there are several reports about the bandgap tuning of C₃N via stacking or forming nanoribbon, bandgap modulation of bilayer C₃N nanoribbons (C₃NNRs) with various edge structures is still far from well understood. Here, based on extensive first-principles calculations, we demonstrated the effective bandgap engineering of C₃N by cutting it into hydrogen passivated C₃NNRs and stacking them into bilayer heterostructures. It was found that armchair (AC) C₃NNRs with three types of edge structures are all semiconductors, while only zigzag (ZZ) C₃NNRs with edges composed of both C and N atoms (ZZCN/ CN) are semiconductors. The bandgaps of all semiconducting C₃NNRs are larger than that of C₃N nanosheet. More interestingly, AC-C₃NNRs with CN/CN edges (AC-CN/CN) possess direct bandgap while ZZ-CN/CN have indirect bandgap. Compared with the monolayer C₃NNR, the bandgaps of bilayer C₃NNRs can be greatly modulated via different stacking orders and edge structures, varying from 0.43 eV for ZZ-CN/CN with AB′-stacking to 0.04 eV for AC-CN/CN with AA-stacking. Particularly, transition from direct to indirect bandgap was observed in the bilayer AC-CN/CN heterostructure with AA′-stacking, and the indirect-to-direct transition was found in the bilayer ZZ-CN/CN with ABstacking. This work provides insights into the effective bandgap engineering of C₃N and offers a new opportunity for its applications in nano-electronics and optoelectronic devices.