The electromagnetic wave characteristics in a coaxial adiabatic line were investigated by using the mode matching technique. The Hankel transform and the Fourier series were employed to describe field distributions. A set of simultaneous equations was built by applying boundary conditions. Residue calculus was performed to determine unknown modal coefficients rapidly. Numerically calculated transmission coefficients and reflection coefficients were compared with a commercial radio frequency (RF) simulation tool, CST Microwave Studio (MWS). Our methodology can provide highly accurate results while reducing the elapsed time of calculation.