The method of reverberation-ray matrix (MRRM) is proposed for the analysis of in-plane Floquet wave propagation in general periodic laminated transversely isotropic composites. For this plane strain problem, by introducing the Floquet-Bloch principle, the formulation of MRRM giving the system equations is first derived based on the unit cell of the periodic multilayered media. The dispersion equation, which is used to compute the dispersion curves of the in-plane Floquet waves, is then obtained from vanishing the determinant of coefficient matrix of the system equation. Afterwards the numerical examples are given to illustrate the effectiveness of the proposed method in both low and high frequency range. From the numerical examples, the general features of the frequency-wavenumber spectra of the in-plane Floquet waves are finally summarized. The results obtained in this paper can be used to guide the design of periodic laminated composites for wave and vibration control applications.