Transient analysis of transmission line has recently been received more attention because operating speeds in high-speed digital electronics are increasing. Transmission line equations are hyperbolic partial differential equations, firstly this paper deduces how to change transmission line equations into quasilinear differential equations , thus the transmission line equation numerical result is gotten by computing the differential formation of quasilinear differential equations. The constraint of voltage and current is be considered and lumped equivalent circuit mode at boundary network collaborated at the same time in finding boundary conditions. Finally the paper computes transient response of transmission line with two typical boundary conditions. Numerical result shows that this approach is an effective way. It is explicit algorithm with less CPU consumption which can get time field response directly. The agree-upon effective way does be frequency field method, however it could not get time response unless the numerical inverse laplace transformation (NILT) be introduced. Thus this approach is more effective than FFT algorithm.