In order to improve the sensitivity and reliability of traveling wave protection, a new algorithm for fast protection of double transmission lines on same tower is proposed based on initial current traveling wave phase comparison. In view of calculating initial traveling wave phase based on S-transform, and the protection criterion is constructed by analyzing the phasor relations of the initial current traveling wave at the same end and the opposite end of the same line. The current traveling wave phase of the same end is almost the opposite when the internal single line fault occurs. The current traveling wave phase of the same end is almost the same, and the current traveling wave phase of opposite end of the same line is almost the same when the internal cross line of the same phase fault occurs. When the external fault occurs, the current traveling wave phase of the same end is almost the same, and the current traveling wave phase of opposite end of the same line is almost the opposite. This paper introduces the concept of the phase difference of the traveling wave, and identifies the internal and external faults of the double lines on the same tower by analyzing the changing characteristics of the phase difference of the current traveling wave. A large number of simulation results show that the protection performance is sensitive, reliable, fast and simple criteria. The protection is barely influenced by the initial angle, fault type and transition resistance and other factors. This work is supported by National Natural Science Foundation of China (No. 11705122).