Incipient faults are known as the faults mainly occurring on the junctions of underground power cables. Clearing quickly, these faults are difficult to detect by conventional protection equipment, leading to insulation degradation and permanent fault in the power cable over time. In this paper, employing similarity functions, a new method is put forward to distinguish the existing fault from other similar events with both high speed and accuracy. The proposed algorithm consists of a two-stages algorithm including change detection, disturbance identification, and fault detection. The proposed method performs the calculation on the voltage signal that is recorded at the sending end of the line. The cross-correlation function is employed for identifying change detection and determining disturbance time. Afterward, using sinusoidal curve fitting, the algorithm can distinguish the incipient fault from sudden load change, capacitor switching, and harmonic load. The accuracy of the proposed approach is verified by some experimental data and 6272 simulation data obtained from four types of well-known arc models, capacitor switching, and also load variations.