<p>The study of guided wave dispersion curves has received a lot of attention in recent decades due to their significance in the fields of non-destructive and structural health monitoring applications. This article presents a semi-analytical spectral element (SASE) method using high-order spectral elements for dispersion analysis of functionally graded material (FGM) plates for the first time in the literature. The cross-section is discretized with high-order Gauss–Lobatto–Legendre (GLL) elements. The equation of motion is derived from Hamilton’s principle. The Lobatto quadrature schemes for full exact integration of stiffness and mass matrices and under-integration leading to diagonal mass matrix are determined for FGM plates with power law inhomogeneity. The validation of the proposed SASE method is carried out by comparing it with the published analytical solutions. Comparison of SASE results using fewer high-order GLL elements for an aluminum plate with those of conventional linear and quadratic elements shows that the high-order SASE method has higher accuracy and computational efficiency at high frequencies and for higher modes. Results demonstrate the spectral convergence characteristics of the proposed element for phase velocity prediction even with under-integration using the nodes as integration points. The numerical study also demonstrates faster convergence and excellent accuracy of the proposed method for the analysis of elastic wave propagation in FGM plates. We used the SASE method based on high-order GLL spectral elements to investigate the dispersion behavior in FGM plates. The influence of the inhomogeneity index on dispersion relations and cutoff frequencies for different wave modes is investigated. The presented dispersion curves for FGM plates will serve as a benchmark for assessing the accuracy of other numerical methods for wave propagation analysis.</p>