In this paper, a new algorithm is proposed for faults detection and classification in the power transmission line. The key of the proposed algorithm depends on the computing of the linear regression coefficient indices (LRCIs) of the three‐phase current signals. The proposed algorithm has constructed a rule as follows: when the system is running under the health condition, the LRCIs will be equal to zero; when the system is subjected to the fault condition, the LRCIs of faulted phases will be greater than zero. Different faults circumstances, such as different inception time, different fault resistances, and different locations, have been verified. Additional scenarios such as far‐end fault with high resistance, fault occurred near the terminal, fault considering variable loading angle, and fault at the presence of noise are also discussed. For each possible scenario of faults, the proposed algorithm required only the three‐phase current measurement of the local measurement. The proposed algorithm has demonstrated a reasonable time response, where the fault condition could be detected within a few milliseconds after the fault inception. Therefore, the proposed algorithm is quite suitable for faults detection and classification in power transmission lines. © 2018 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.