C₃N has attracted much attention as an anode material for lithium-ion (Li-ion) batteries, owing to its excellent mechanical and electronic properties. However, its weak Li adsorption strength and mobility have limited its further application. Phosphorene (P) exhibits a high bonding strength with Li and excellent Li-ion mobility, but low stiffness. Thus, we propose that constructing a C₃N/P hybrid material will not only negate the deficiency of C₃N but also result in a new high performance electrode material. A C₃N/P heterostructure is constructed and studied by first-principles calculations. This heterostructure exhibits an excellent stiffness (Young's modulus is 448.32 N m⁻¹), which is even better than that of graphene. The bonding strength of Li inserted into the intralayer of the C₃N/P heterostructure (1.78–2.02 eV) is much higher than that in pristine monolayer C₃N (0.32 eV) and phosphorene (1.67 eV). Moreover, the C₃N/P heterostructure shows a high capacity of 468.34 mA h g⁻¹, and better conductivities of electricity and ions than pristine monolayer C₃N. The excellent mechanical properties, high capacity, good conductivities of electrons and ions and moderately high bonding energy indicate that the C₃N/P heterostructure is a promising anode material for lithium-ion batteries.