The Fourier series expansion method is a useful tool to approach the problems of discontinuities in optical waveguides, and it can apply to analyze the Floquet-modes of photonic crystal waveguides. However, it has known that the Floquet-mode calculation with large truncation order is limited because of the roundoff errors. This paper proposes a novel formulation of the Floquet-modes propagating in two-dimensional photonic crystal waveguides formed by circular cylinders. We introduce a periodic boundary condition as same with the conventional method, and the fields are expressed in the Fourier series expansions. The present formulation also introduces the cylindrical-wave expansions and uses the recursive transition-matrix algorithm, which is used to analyze the scattering from cylinder array. This makes us possible to obtain very high accuracy without the use of large truncation order for Fourier series expansion. The presented formulation is validated by numerical experiments.