The cylindrical Taylor Interpolation through FFT (TI-FFT) algorithm for computation of the near-field and far-field in the quasi-cylindrical geometry has been introduced. The modal expansion coefficient of the vector potentials ${\bf F}$ and ${\bf A}$ within the context of the cylindrical harmonics (TE and TM modes) can be expressed in the closed-form expression through the cylindrical addition theorem. For the quasi-cylindrical geometry, the modal expansion coefficient can be evaluated through FFT with the help of the Taylor Interpolation (TI) technique. The near-field on any arbitrary cylindrical surface can be obtained through the Inverse Fourier Transform (IFT). The far-field can be obtained through the Near-Field Far-Field (NF-FF) transform. The cylindrical TI-FFT algorithm has the advantages of $\mathcal{O} \left( \hbox{N} \log_2 \hbox{N} \right)$ computational complexity for $\hbox{N} = \hbox{N}_φ\times \hbox{N}_z$ computational grid, small sampling rate (large sampling spacing) and no singularity problem.