Attention deficit hyperactivity disorder is one of the common neurodevelopmental disorders that appears early in childhood and often persists into adulthood if timely and appropriate interventions are not implemented. Therefore, the early and timely diagnosis of attention deficit hyperactivity disorder (ADHD) in children plays an extremely important role in the process of controlling and improving symptoms. The current diagnosis of ADHD is still only a clinical diagnosis, which requires a long observation time and a rather complicated process. However, since electroencephalography (EEG) was proposed, researched, and tested in detecting ADHD patients, it has provided many valuable insights and proved to be extremely useful, particularly in assessing the neurological functions of children with ADHD. This study focuses on examining the suitability of several spectral estimation methods such as Periodogram, Welch’s method, and Multitaper, when combined with machine learning algorithms in identifying ADHD patients. The EEG signal’s nonlinear neural dynamic properties, including complexity and entropy, are also exploited and evaluated through classification models. Linear Discriminant Analysis (LDA), Support Vector Machine (SVM), and Random Forest (RF) are three machine learning algorithms used throughout this study. The results show that the Periodogram spectral estimation method, when used in conjunction with the Support Vector Machine model, yields the best results, additionally, the integration of nonlinear dynamic properties proves to be truly effective, with the constructed classification model achieving an accuracy of 94.3% and an F1-score of 93.8%.