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A complex domain projection method of analysis is proposed based on the transient representation of electro-magnetic traveling wave (EM) for transmission line. Considering the impact of distributed parameters and the characteristics of electro-magnetic wave, the transmission line model is built. The instantaneous voltage equation and the fault location function are derived and obtained and the former is researched for complex domain projection, which is the improvement of orthogonal projection. And the voltage is approached exactly. The edge effect caused by orthogonal scaling function is solved. Complex orthogonal projection transformation can not be affected by the calculation step, which takes advantages of algebra instead and time-invariant matrix Z0 and Y0, as to speed calculating offline. In addition, diagonalization of H is simple and obvious with sparsity. Without convolution, the efficiency and accuracy has been proved, and the adaptive calculation for the sampling frequency through simulation and analysis.