C₃B monolayer is a typical graphene-like two-dimensional material, which has been successfully prepared experimentally. Here, we use the density functional theory to study the structural stability, electronic properties and physical regulation effects of its armchair-edged nanoribbons. The results show that for the bare-edged nanoribbons, if the ribbon edges are composed of C atoms completely (AA-type), their electronic phase is a semiconductor; when both ribbons edges consist of C and B atoms (BB-type) jointly, their electronic phase is a metal; if one edge of the ribbon is composed of C atoms and the other edge is comprised of B and C atoms (AB-type), their electronic phase is also a metal. This suggests that the B atom located at the ribbon edge plays an important role in determining whether nanoribbons is a metal or semiconductor. While for the H-terminated nanoribbons, they are all direct or indirect band-gap semiconductors. The carrier mobility of H-terminated nanoribbons is generally lower than that of bare-edged nanoribbon, which is closely related to their larger effective mass and higher deformation potential values. Meanwhile, it is found that the semiconducting nanoribbons are very sensitive to physical regulation, especially under applied compressive strain and external electric field, the band gap of the nanoribbons becomes very smaller, which is favorable for the absorption of light energy and development of novel optical devices.