Travelling wave protection is a research hotspot of relay protection in electric power system, but the low reliability of travelling wave protection has been hindering its practical application in AC power grid. The effect of fault initial phase angle and fault resistance on faulty travelling wave was found to be an important reason for its low reliability. In this paper, we proposed a new traveling current protection method for transmission line based on the Hilbert-Huang transform, fault initial phase angle and fault resistance. HHT is firstly applied to decomposing the instantaneous amplitudes of the first IMFs of two lines that connected to one identical bus, upon which integrations are carried out. The integral difference of two instantaneous amplitudes is then used to calculate the transition resistance and fault initial angle. The normalised integral difference is defined as the fault characteristic variable, which can be used to determine whether the fault exists inside area or outside area. This work presents a solution that not only removes the influence of fault beginning angle and fault resistance on transient protection, but also avoids the effect of multiple components in the transient signal on protection, which improving protection reliability. The proposed algorithm owns a protection area as twice as that of those traditional methods. The validity of the proposed algorithm has been confirmed using ATP-Draw simulation in a three-phase 500 kV power system with various types of faults.