This paper explains how to convert a distributed-parameter model of an unsymmetrical transmission line for specific boundary conditions into a system of Ordinary Differential Equations (ODEs). This approach can be used to study switching transients on transmission lines or to develop new algorithms for line parameter identification. The main technique in the process of model conversion is spatial discterization achieved by using the Chebyshev pseudo-spectral method. The key quality of this approach lies in the application of the Lagrange polynomial interpolation with barycentric weights to represent change of a variable in space and to formulate operators for spatial derivatives. Approximation accuracy for a specific spatial grid resolution can be determined by evaluating coefficients of the Chebyshev polynomial expansion. These are computed from the Lagrange interpolation using Discrete Cosine Transform (DCT). The numerical example is presented to demonstrate application of the method in simulating distributed-parameter unsymmetrical lines during switching events.