Motivated by the recent synthesis of the graphene-like C3N nanosheet, the geometrical structures and electronic properties of its ribbon form, that is, C3N nanoribbons (C3NNRs), are investigated by first-principles calculations. It is found that there are five types of energetically favorable H-terminated edges in the C3NNRs. Different from graphene nanoribbons, the corresponding stable C3NNRs are all nonmagnetic semiconductors regardless of the edge shape and termination. However, their band feature and gap size can be modulated by the ribbon width and edge termination, which brings direct-, quasi-direct-, and indirect-band-gap semiconducting behaviors in the nanoribbons. Comparing to the C3N nanosheet, the work function is reduced in the C3NNRs with fully di- and monohydrogenated edges, which results in a type-II band alignment with SiC and silicane nanosheets. More interestingly, the combined hetero-nanostructures will be promising excitonic solar cell materials with high power conversion efficiencies up to 17–21%. Our study demonstrates that the C3NNRs have distinct edge stabilities and variable semiconducting behaviors, which endow fascinating potential applications in the fields of solar energy and nanodevices.