A numerical technique based on Haar wavelets is used for solving transient problems of transmission lines. The approach of our method is to convert the original coupled partial differential equations, the transmission line equations or the telegrapher equations, to a system of ordinary matrix differential equations via Haar wavelets. Then, transient problems of transmission lines can be solved by matrix operations. Numerical examples of homogeneous and dispersive lines, along with both linear and nonlinear loads are verified. In addition, non-sinusoidal signals such as the unit step function and the rectangular pulse for digital applications are included to demonstrate the use of this efficient, easy-to-handle, stable, and versatile method.