Nd-Fe-C alloys have been reported as hard magnetic materials with a potential higher coercivity than Nd-Fe-B alloys. However, it has been seldom studied since its intrinsic properties were investigated in the last century. Here, we revisited the structure, phase precipitation and magnetic properties of rapidly quenched ternary Nd-Fe-C alloys for further understanding their composition-microstructure-property relationships. The Nd10+xFe84−xC6 (x = −2, 0, 2, 3, 4, 5) alloys with various compositions were prepared by melt spinning. The results show that the hard magnetic Nd2Fe14C phase can be hardly formed in the as-spun alloys. Instead, the alloys are composed of soft magnetic α-Fe phase and planar anisotropic Nd2Fe17Cx phase. After annealing above 650 °C, the Nd2Fe14C phase is precipitated by the peritectoid reaction. All optimally annealed alloys contain Nd2Fe14C and Nd2Fe17Cx phases, while the presence and content of α-Fe phase are determined by the alloy composition. The crystallization degree of the as-spun alloys has an effect on their magnetic properties after annealing. After the annealing treatment, partly crystallized as-spun alloys exhibit better magnetic properties than the amorphous alloys. The intrinsic coercivity Hcj = 847 kA/m, remanence Jr = 0.69 T, and maximum energy product (BH)max = 64.3 kJ/m3 were obtained in the Nd14Fe80C6 alloy annealed at 725 °C. The formation of the Nd2Fe14C and Nd2Fe17Cx phases with the Nd2O3 phase precipitated at the triangular grain boundaries is responsible for its relatively good properties. Although the magnetic properties of Nd-Fe-C alloys obtained in this work are inferior to those of Nd-Fe-B, the present results help us to further understand the magnetic behavior of Nd-Fe-C alloys.