As one of the most promising technologies, ultrasonic Lamb waves have been widely analyzed in the non-destructive evaluation. However, due to the guided dispersion and mode overlap, mode identification and dispersion determination are still challenging, thereby attacting considerable attentions. Here, we use two traditional spectrum estimation methods, i.e., the Yule-Walker method and the Burg method to analyze the array-transducer signals for high-resolution ultrasonic Lamb waves dispersion measurement. An inverse method was also designed to estimate the aluminum plate thickness from the extracted wideband dispersion curves. Experiments on three aluminate plates with different thicknesses (3 mm, 4 mm and 5 mm) demonstrated that the spectrum estimation methods were helpful for the ultrasonic Lamb waves based non-destructive evaluation.