Abstract: Based on linear three-dimensional elasticity, the wave motion equations for coupled longitudinal guided waves are derived by using a Legendre orthogonal polynomial approach, and the coupled equations of wave motion are solved numerically. Firstly, to determine the applicability and accuracy of this method, the dispersion curves of longitudinal guided waves in isotropic hollow cylinders were solved by using Disperse software. The results obtained by Disperse calculation are compared with those by Legendre orthogonal polynomial approach method. The calculation results of the two methods are consistent. Then, the influence of the Legendre polynomial cutoff value on the convergence of the axisymmetric guided wave dispersion curves is discussed. The reason of the influence is analyzed by the numerical calculation. Finally, for the composite hollow cylinder wound by carbon fiber, the dispersion curves of three different modes of longitudinal guided waves are calculated separately. The phase velocity dispersion curves for different ratios of outer radius to thickness are calculated to analyze the influence of the ratio on the dispersion curves.